diff --git a/src/lib/classify.ml b/src/lib/classify.ml
index cc7bfcc..22d6069 100644
--- a/src/lib/classify.ml
+++ b/src/lib/classify.ml
@@ -60,7 +60,7 @@ module type Classifier_intf = sig
   val eval : t -> feature -> clas probabilities
 
   type samples = (clas * feature) list
-  val estimate : ?spec:spec -> ?classes:clas list -> samples -> t
+  val estimate : ?opt:opt -> ?classes:clas list -> samples -> t
 end
 
 module type Generative_intf = sig
@@ -136,7 +136,7 @@ let estimate_naive_bayes modulename (type c) init update incorporate
 module BinomialNaiveBayes(Data: Dummy_encoded_data_intf)
   : (Generative_intf with type feature = Data.feature
                      and type clas = Data.clas
-                     and type spec = binomial_spec)
+                     and type opt = binomial_spec)
   = struct
 
   type feature = Data.feature
@@ -174,12 +174,12 @@ module BinomialNaiveBayes(Data: Dummy_encoded_data_intf)
     in
     eval_naive_bayes ~to_prior ~to_likelihood nb.table
 
-  type spec = binomial_spec
+  type opt = binomial_spec
   let default = { smoothing = 0.0; bernoulli = false }
 
   module Cm = Map.Make(struct type t = clas let compare = compare end)
 
-  let estimate ?(spec=default) ?classes data =
+  let estimate ?(opt=default) ?classes data =
     let aa = Data.size + 1 in
     let init _cls = Array.make aa 0 in
     let update arr ftr =
@@ -190,7 +190,7 @@ module BinomialNaiveBayes(Data: Dummy_encoded_data_intf)
       arr
     in
     let incorporate all num_classes totalf =
-      let to_prob = smoothing_to_prob spec.smoothing in
+      let to_prob = smoothing_to_prob opt.smoothing in
       List.map all ~f:(fun (cl, attr_count) ->
         let prior_count = float attr_count.(Data.size) in
         let likelihood =
@@ -206,7 +206,7 @@ module BinomialNaiveBayes(Data: Dummy_encoded_data_intf)
       estimate_naive_bayes "BinomialNaiveBayes"
         init update incorporate (module Cm) ?classes data
     in
-    {table ; e_bernoulli = spec.bernoulli}
+    {table ; e_bernoulli = opt.bernoulli}
 
   let class_probabilities nb cls =
     let arr = List.assoc cls nb.table in
@@ -235,7 +235,7 @@ type smoothing = float
 module CategoricalNaiveBayes(Data: Category_encoded_data_intf)
   : (Generative_intf with type feature = Data.feature
                      and type clas = Data.clas
-                     and type spec = smoothing)
+                     and type opt = smoothing)
 
   = struct
 
@@ -274,12 +274,12 @@ module CategoricalNaiveBayes(Data: Category_encoded_data_intf)
     in
     eval_naive_bayes ~to_prior ~to_likelihood table
 
-  type spec = smoothing
+  type opt = smoothing
   let default = 0.0
 
   module Cm = Map.Make(struct type t = clas let compare = compare end)
 
-  let estimate ?(spec=default) =
+  let estimate ?(opt=default) =
     let init _ = (0, Array.map (fun i -> Array.make i 0) Data.encoding_sizes) in
     let update (c, arr) ftr =
       let ftr_arr = safe_encoding ftr in
@@ -287,7 +287,7 @@ module CategoricalNaiveBayes(Data: Category_encoded_data_intf)
       (c + 1, arr)
     in
     let incorporate all num_classes totalf =
-      let to_prob = smoothing_to_prob spec in
+      let to_prob = smoothing_to_prob opt in
       List.map all ~f:(fun (cl, (class_count, attr_count)) ->
         let prior      = to_prob (float class_count) totalf (float num_classes) in
         let likelihood =
@@ -322,7 +322,7 @@ let to_safe_encoding_size_checked interfacename size encoding f =
 module GaussianNaiveBayes(Data: Continuous_encoded_data_intf)
   : (Generative_intf with type feature = Data.feature
                      and type clas = Data.clas
-                     and type spec = unit)
+                     and type opt = unit)
 
   = struct
 
@@ -353,13 +353,13 @@ module GaussianNaiveBayes(Data: Continuous_encoded_data_intf)
     in
     eval_naive_bayes ~to_prior ~to_likelihood table
 
-  type spec = unit
+  type opt = unit
   let default = ()
 
   module Cm = Map.Make(struct type t = clas let compare = compare end)
 
-  let estimate ?(spec=default) =
-    ignore spec;
+  let estimate ?(opt=default) =
+    ignore opt;
     let init _c = (0, Array.make Data.size Running.empty) in
     let update (c, rs_arr) ftr =
       let attr = safe_encoding ftr in
@@ -396,7 +396,7 @@ module LrCommon(Data: Continuous_encoded_data_intf) = struct
 
   type samples = (clas * feature) list
 
-  type spec = log_reg_spec
+  type opt = log_reg_spec
   let default = { lambda = 1e-4
                 ; tolerance = 1e4
                 }
@@ -408,7 +408,7 @@ module LrCommon(Data: Continuous_encoded_data_intf) = struct
   let copy1 arr = Array.init (Data.size + 1) (function | 0 -> 1. | i -> arr.(i - 1))
 
   (* map classes to [1;2 ... 3], convert features to matrix and run Softmax *)
-  let estimate ~method_name ~class_bound ~to_t ?(spec=default) ?(classes=[]) data =
+  let estimate ~method_name ~class_bound ~to_t ?(opt=default) ?(classes=[]) data =
     let class_bound =
       match class_bound with
       | None   -> fun n -> n
@@ -444,8 +444,8 @@ module LrCommon(Data: Continuous_encoded_data_intf) = struct
         in
         let weights =
           Softmax_regression.regress
-            ~lambda:spec.lambda
-            ~tolerance:spec.tolerance
+            ~lambda:opt.lambda
+            ~tolerance:opt.tolerance
             ftrs classes
         in
         let sortedc =
@@ -461,7 +461,7 @@ module LogisticRegression(Data: Continuous_encoded_data_intf)
   : sig
     include Classifier_intf with type feature = Data.feature
                             and type clas = Data.clas
-                            and type spec = log_reg_spec
+                            and type opt = log_reg_spec
 
     val coefficients : t -> float array
 
@@ -504,7 +504,7 @@ module MulticlassLogisticRegression(Data: Continuous_encoded_data_intf)
   : sig
     include Classifier_intf with type feature = Data.feature
                             and type clas = Data.clas
-                            and type spec = log_reg_spec
+                            and type opt = log_reg_spec
 
     val coefficients : t -> float array array
 
diff --git a/src/lib/classify.mli b/src/lib/classify.mli
index 2b0fb32..4088596 100644
--- a/src/lib/classify.mli
+++ b/src/lib/classify.mli
@@ -109,7 +109,7 @@ module type Classifier_intf = sig
   (** Representing training data. *)
   type samples = (clas * feature) list
 
-  (** [estimate spec classes samples] estimates a classifier based upon the
+  (** [estimate opt classes samples] estimates a classifier based upon the
       training [samples].
 
       [classes] is an optional argument to specify ahead of time the possible
@@ -117,14 +117,14 @@ module type Classifier_intf = sig
       This is useful for models where we know the population domain but may
       not see an example of a training datum for rare cases.
 
-      [spec] are the optional classifier dependent estimation/evaluation
+      [opt] are the optional classifier dependent estimation/evaluation
       arguments.
 
       @raise Invalid_argument if [classes] are specified and new ones are
       found in the training [samples].
       @raise Invalid_argument if [samples] is empty.
   *)
-  val estimate : ?spec:spec -> ?classes:clas list -> samples -> t
+  val estimate : ?opt:opt -> ?classes:clas list -> samples -> t
 end
 
 (** A generative classifier builds models of the form
@@ -172,7 +172,7 @@ type binomial_spec =
   classifier on data encoded using
   {{!modtype:Dummy_encoded_data_intf}Dummy variables.} *)
 module BinomialNaiveBayes(D: Dummy_encoded_data_intf) :
-  Generative_intf with type spec = binomial_spec
+  Generative_intf with type opt = binomial_spec
                   and type feature = D.feature
                   and type clas = D.clas
 
@@ -181,7 +181,7 @@ module BinomialNaiveBayes(D: Dummy_encoded_data_intf) :
   classifier on data encoded using
   {{!modtype:Category_encoded_data_intf}Categorical variables.} *)
 module CategoricalNaiveBayes(D: Category_encoded_data_intf) :
-  Generative_intf with type spec = smoothing
+  Generative_intf with type opt = smoothing
                   and type feature = D.feature
                   and type clas = D.clas
 
@@ -191,7 +191,7 @@ module CategoricalNaiveBayes(D: Category_encoded_data_intf) :
   for each of the quantitative features in the
   {{!modtype:Continuous_encoded_data_intf}encoded data}. *)
 module GaussianNaiveBayes(D: Continuous_encoded_data_intf) :
-  Generative_intf with type spec = unit
+  Generative_intf with type opt = unit
                   and type feature = D.feature
                   and type clas = D.clas
 
@@ -230,7 +230,7 @@ type log_reg_spec =
 *)
 module LogisticRegression(D: Continuous_encoded_data_intf) :
   sig
-    include Classifier_intf with type spec = log_reg_spec
+    include Classifier_intf with type opt = log_reg_spec
                             and type feature = D.feature
                             and type clas = D.clas
 
@@ -259,7 +259,7 @@ module LogisticRegression(D: Continuous_encoded_data_intf) :
 *)
 module MulticlassLogisticRegression(D: Continuous_encoded_data_intf) :
   sig
-    include Classifier_intf with type spec = log_reg_spec
+    include Classifier_intf with type opt = log_reg_spec
                              and type feature = D.feature
                              and type clas = D.clas
 
diff --git a/src/lib/classify.mlt b/src/lib/classify.mlt
index 1e2510a..01de036 100644
--- a/src/lib/classify.mlt
+++ b/src/lib/classify.mlt
@@ -58,7 +58,7 @@ let () =
           let size = 5
         end)
       in
-      let naiveb = NB.estimate ~spec:{NB.default with bernoulli = true } data in
+      let naiveb = NB.estimate ~opt:{NB.default with bernoulli = true } data in
       let sample = [ `shortbread ; `whiskey; `porridge  ] in
       let result = NB.eval naiveb sample in
       let expect =
diff --git a/src/lib/regression.ml b/src/lib/regression.ml
index bb6242d..fe3f1f6 100644
--- a/src/lib/regression.ml
+++ b/src/lib/regression.ml
@@ -30,7 +30,7 @@ module type Linear_model_intf = sig
   val describe : t -> string
 
   val eval : t -> input -> float
-  val regress : ?spec:spec -> input array -> resp:float array -> t
+  val regress : ?opt:opt -> input array -> resp:float array -> t
 
   val residuals : t -> float array
   val coefficients : t -> float array
@@ -63,7 +63,7 @@ module Univariate = struct
     ; inferred_var     : float          (* inferred variance of error. *)
     ; s_yy             : float          (* sum of diff or resp to mean, TSS. *)
     ; s_xx             : float          (* sum of diff of pred to mean. *)
-    ; goodness_of_fit  : float option
+    (*; goodness_of_fit  : float option *)
     }
 
   let alpha lrm = lrm.alpha
@@ -82,23 +82,23 @@ module Univariate = struct
 
   let eval lrm x = lrm.alpha +. lrm.beta *. x
 
-  type spec = float array
+  type opt = float array
 
-  let default = [||]
+  let opt ?weights () = match weights with | None -> [||] | Some a -> a
 
-  let regress ?spec pred ~resp =
+  let default = opt ()
+
+  let regress ?(opt=default) pred ~resp =
     let n = Array.length pred in
-    (* Optional spec argument allows us to specify the individual error
+    (* Optional argument allows us to specify the individual error
        weights on each observation. *)
+    let an = Array.length opt in
     let weights =
-      match spec with
-      | None   -> Array.make n 1.0
-      | Some a ->
-          let an = Array.length a in
-          if an <> n then
-            invalidArg "regress: spec length %d <> d predictor size %d" an n
-          else
-            a
+      if an = 0 then Array.make n 1.0
+      else if an <> n then
+        invalidArg "regress: opt length %d <> d predictor size %d" an n
+      else
+        opt
     in
     let w_s = Array.sumf weights in
     let sum2 f a1 a2 =
@@ -119,11 +119,11 @@ module Univariate = struct
     let srs = sum2 (fun w_i r -> w_i *. r *. r) weights rss in
     (* degress of freedom: one for the constant and one for beta *)
     let dgf = float (n - 2) in
-    let q =
-      match spec with
+    (*let q =
+      match opt with
       | None   -> None
       | Some _ -> Some (Functions.chi_square_greater (truncate dgf) srs)
-    in
+    in*)
     { m_pred
     ; m_resp
     ; size = float n
@@ -133,7 +133,7 @@ module Univariate = struct
     ; residuals = rss
     ; sum_residuals = srs
     ; inferred_var = srs /. dgf
-    ; goodness_of_fit = q
+    (*; goodness_of_fit = q *)
     ; s_yy = sum2 ( *. ) d_y d_y
     ; s_xx = d_xx_w
     }
@@ -176,15 +176,6 @@ module Univariate = struct
 
 end
 
-type lambda_spec =
-  | Spec of float
-  | From of float array
-
-type multivariate_spec =
-  { add_constant_column : bool
-  ; lambda_spec : lambda_spec option
-  }
-
 (* 'Solved' (via SVD) linear problem. *)
 type solved_lp =
   { coef : vec
@@ -197,20 +188,20 @@ module SolveLPViaSvd = struct
 
   open Lacaml_util
 
-  let to_lambda f g lambda_spec =
+  let to_lambda f g l2_regularizer =
     let bestl =
-      match lambda_spec with
-      | Spec l -> l
-      | From arr ->
+      match l2_regularizer with
+      | `S l -> l
+      | `From arr ->
           let loess = Array.map (fun l -> l, g (f l)) arr in
           Array.sort (fun (_,s1) (_,s2) -> compare s1 s2) loess;
           fst loess.(0)
     in
     bestl, f bestl
 
-  let reg_to_lambda svd resp lambda_spec =
+  let reg_to_lambda svd resp l2_regularizer =
     let looe  = Svd.looe svd resp in
-    to_lambda looe Vec.ssqr lambda_spec
+    to_lambda looe Vec.ssqr l2_regularizer
 
   let full_looe cmi pred resi =
     let h  = gemm (gemm pred cmi) ~transb:`T pred in
@@ -238,7 +229,7 @@ module SolveLPViaSvd = struct
         ; resi
         ; looe
         }
-    | Some lambda_spec ->
+    | Some l2_regularizer ->
         match pred with
         | `Unpadded p ->
             let dcp = lacpy p in
@@ -246,7 +237,7 @@ module SolveLPViaSvd = struct
             (* Odd, that we should know the error on the coefficients
               _before_ computing them! There's probably a better way to
               structure this! *)
-            let lambda, looe = reg_to_lambda svd resp lambda_spec in
+            let lambda, looe = reg_to_lambda svd resp l2_regularizer in
             let coef = Svd.solve_linear ~lambda svd resp in
             { coef
             ; vaco = `Svd svd
@@ -255,7 +246,7 @@ module SolveLPViaSvd = struct
             }
         | `Padded (orig, fill) ->
             let svd = Svd.svd orig in
-            let lambda, _ = reg_to_lambda svd resp lambda_spec in
+            let lambda, _ = reg_to_lambda svd resp l2_regularizer in
             let coef = Svd.solve_linear ~lambda svd resp in
             (* Set the constant term beta to the mean of the response.
               See "Estimation of the constant term when using ridge regression"
@@ -383,14 +374,18 @@ end
 
 module Multivariate = struct
 
+  type opt =
+    { add_constant_column : bool          (** Instructs the method to efficiently insert a colum of 1's into the
+                                            design matrix for the constant term. *)
+    ; l2_regularizer : [`S of float | `From of float array] option    (** How to optionally determine the ridge parameter. *)
+    }
+
   include EvalMultiVarite
 
-  type spec = multivariate_spec
+  let opt ?l2_regularizer ?(add_constant_column=true) () =
+    { add_constant_column ; l2_regularizer }
 
-  let default =
-    { add_constant_column = false
-    ; lambda_spec = None
-    }
+  let default = opt ()
 
   open Lacaml_util
   open SolveLPViaSvd
@@ -420,9 +415,9 @@ module Multivariate = struct
     - work through these covariance matrix calculations, they're probably not right
     - once that's done we can expose the hypothesis testing
   *)
-  let regress ?(spec=default) pred ~resp =
+  let regress ?(opt=default) pred ~resp =
     let resp = Vec.of_array resp in
-    let pad = spec.add_constant_column in
+    let pad = opt.add_constant_column in
     let pred, num_obs, num_pred, across_pred_col = pad_design_matrix pred pad in
     (* TODO: replace with folds, across the matrix in Lacaml. *)
     let num_obs_float = float num_obs in
@@ -431,7 +426,7 @@ module Multivariate = struct
     let m_pred        = across_pred_col (col_mean num_obs_float) in
     (* since num_pred includes a value for the constant coefficient, no -1 is needed. *)
     let deg_of_freedom  = float (num_obs - num_pred) in
-    let lambda          = spec.lambda_spec in
+    let lambda          = opt.l2_regularizer in
     let solved_lp       = solve_lp pred resp lambda in
     let sum_residuals   = dot solved_lp.resi solved_lp.resi in
     let inferred_var  = sum_residuals /. deg_of_freedom in
@@ -454,28 +449,26 @@ module Multivariate = struct
 
 end
 
-type tikhonov_spec =
-  { regularizer : float array array
-  ; lambda_spec : lambda_spec option (* multipliers on the regularizing matrix. *)
-  }
-
 module Tikhonov = struct
 
+  type opt =
+    { tik_matrix : float array array   (** The regularizing matrix. *)
+    ; l2_regularizer : [`S of float | `From of float array] option  (** How to optionally determine the ridge parameter. *)
+    }
+
   include EvalMultiVarite
 
-  type spec = tikhonov_spec
+  let opt ?(tik_matrix = [|[||]|]) ?l2_regularizer () =
+    { tik_matrix ; l2_regularizer }
 
-  let default =
-    { regularizer = [|[||]|]
-    ; lambda_spec = None
-    }
+  let default = opt ()
 
   open Lacaml_util
   open SolveLPViaSvd
 
-  let gtr_to_lambda fit_model lambda_spec =
+  let gtr_to_lambda fit_model l2_regularizer =
     let g slp = Vec.ssqr slp.looe in
-    to_lambda fit_model g lambda_spec
+    to_lambda fit_model g l2_regularizer
 
   (* TODO: This method can be optimized if we use a different decomposition. *)
   let gtk_solve_lp pred resp tik = function
@@ -487,7 +480,7 @@ module Tikhonov = struct
         let resi = Vec.sub resp (gemv pred coef) in
         let looe = full_looe covm pred resi in
         { coef ; vaco = `Cov covm ; resi ; looe}
-    | Some lambda_spec ->
+    | Some l2_regularizer ->
         let covm = gemm ~transa:`T pred pred in
         let eval l =
           let copy = lacpy covm in
@@ -498,17 +491,16 @@ module Tikhonov = struct
           let looe = full_looe covm pred resi in
           { coef ; vaco = `Cov covm ; resi ; looe}
         in
-        let lambda, slp = gtr_to_lambda eval lambda_spec in
+        let lambda, slp = gtr_to_lambda eval l2_regularizer in
         let _ = P.printf "chose gtr lambda of %0.4f\n" lambda in
         slp
 
-  let regress ?(spec=default) pred ~resp =
+  let regress ?(opt=default) pred ~resp =
     let pred = Mat.of_array pred in
     let resp = Vec.of_array resp in
-    (* UGH, awkard! to silence 41, need to 'modularize' these *)
-    let lambda = (spec:tikhonov_spec).lambda_spec in
+    let lambda = opt.l2_regularizer in
     let tik =
-      match spec.regularizer with
+      match opt.tik_matrix with
       | [|[||]|] -> Mat.make0 (Mat.dim1 pred) (Mat.dim2 pred)
       | tm       -> Mat.of_array tm
     in
diff --git a/src/lib/regression.mli b/src/lib/regression.mli
index 5c42489..b2df88c 100644
--- a/src/lib/regression.mli
+++ b/src/lib/regression.mli
@@ -32,8 +32,8 @@ module type Linear_model_intf = sig
 
   (** [regress options pred resp] computes a linear model of [resp] based
       off of the independent variables in the design matrix [pred], taking
-      into account the various method [spec]s. *)
-  val regress : ?spec:spec -> input array -> resp:float array -> t
+      into account the various method [opt]s. *)
+  val regress : ?opt:opt -> input array -> resp:float array -> t
 
   (** [residuals t] returns the residuals, the difference between the observed
       value and the estimated value for the independent, response, values. *)
@@ -71,17 +71,21 @@ module type Linear_model_intf = sig
 
 end
 
-(** Simple one dimensional regress. *)
+(** Simple one dimensional regression. *)
 module Univariate : sig
 
+  (** The optional [opt] for univariate regression are weights for each
+      observation. One can use them to change the model such that each
+      error (e_i) is now sampled from it's own distribution: [N(0, s/w_i)],
+      where s^2 is the error variance and w_i is the weight of the ith
+      error. *)
+  type opt = float array
+
+  val opt : ?weights:float array -> unit -> opt
+
   include Linear_model_intf
     with type input = float
-    (** The optional [spec] for univariate regression are weights for each
-        observation. One can use them to change the model such that each
-        error (e_i) is now sampled from it's own distribution: [N(0, s/w_i)],
-        where s^2 is the error variance and w_i is the weight of the ith
-        error. *)
-    and type spec = float array
+    and type opt := opt
 
   (** [alpha t] a shorthand for the constant parameter used in the regression.
       Equivalent to [(coefficients t).(0)] *)
@@ -101,22 +105,23 @@ module Univariate : sig
 
 end
 
-type lambda_spec =
-  | Spec of float         (** Use this specific value. *)
-  | From of float array   (** Choose the value in the array with the lowest Leave-One-Out-Error. *)
+(** Multi-dimensional input regression, with support for Ridge regression. *)
+module Multivariate : sig
 
-type multivariate_spec =
-  { add_constant_column : bool          (** Instructs the method to efficiently insert a colum of 1's into the
+  type opt =
+    { add_constant_column : bool          (** Instructs the method to efficiently insert a colum of 1's into the
                                             design matrix for the constant term. *)
-  ; lambda_spec : lambda_spec option    (** How to optionally determine the ridge parameter. *)
-  }
+    ; l2_regularizer : [`S of float | `From of float array] option    (** How to optionally determine the ridge parameter. *)
+    }
 
-(** Multi-dimensional input regression, with support for Ridge regression. *)
-module Multivariate : sig
+  val opt : ?l2_regularizer:[`S of float | `From of float array] ->
+            ?add_constant_column:bool ->
+            unit ->
+            opt
 
   include Linear_model_intf
     with type input = float array
-    and type spec = multivariate_spec
+    and type opt := opt
 
   (** [aic linear_model] return the Akaike information criterion for the
       [linear_model].*)
@@ -128,11 +133,6 @@ module Multivariate : sig
 
 end
 
-type tikhonov_spec =
-  { regularizer : float array array   (** The regularizing matrix. *)
-  ; lambda_spec : lambda_spec option  (** How to optionally determine the ridge parameter. *)
-  }
-
 (** Multi-dimensional input regression with a matrix regularizer.
   described {{:https://en.wikipedia.org/wiki/Tikhonov_regularization} here}.
 
@@ -140,9 +140,19 @@ type tikhonov_spec =
   been verified. A warning is printed to standard-error. *)
 module Tikhonov : sig
 
+  type opt =
+    { tik_matrix : float array array   (** The regularizing matrix. *)
+    ; l2_regularizer : [`S of float | `From of float array] option  (** How to optionally determine the ridge parameter. *)
+    }
+
+  val opt : ?tik_matrix:float array array ->
+            ?l2_regularizer:[`S of float | `From of float array] ->
+            unit ->
+            opt
+
   include Linear_model_intf
     with type input = float array
-    and type spec = tikhonov_spec
+    and type opt := opt
 
   (** [aic linear_model] return the Akaike information criterion for the
       [linear_model].*)
diff --git a/src/lib/regression.mlt b/src/lib/regression.mlt
index bcc03ac..4f9d3c0 100644
--- a/src/lib/regression.mlt
+++ b/src/lib/regression.mlt
@@ -31,12 +31,8 @@ let looe_manually lambda pred resp =
   pred
   |> Array.mapi (fun i p ->
     let p_pred, p_resp = without i in
-    let ms =
-      { add_constant_column = false
-      ; lambda_spec = Some (Spec lambda)
-      }
-    in
-    let model = M.regress ~spec:ms p_pred ~resp:p_resp in
+    let opt   = M.opt ~add_constant_column:false ~l2_regularizer:(`S lambda) () in
+    let model = M.regress ~opt p_pred ~resp:p_resp in
     resp.(i) -. M.eval model p)
 
 (* Testing the accuracy of numerical algorithms is hard (and fun).
@@ -131,7 +127,7 @@ let () =
     ~title:"General can recover coefficients."
     Gen.(general_model 1e11 ~max_samples ~max_predictors)
     (fun (pred, coef, resp) ->
-      let glm = M.regress ~resp pred in
+      let glm = M.(regress ~opt:(opt ~add_constant_column:false ()) ~resp pred) in
       Vectors.equal ~d:1e-2 (M.coefficients glm) coef)
     Spec.([just_postcond_pred is_true]);
 
@@ -142,7 +138,7 @@ let () =
       let glm = M.regress ~resp pred in
       let r0 = (M.residuals glm).(0) in
       let e0 = resp.(0) -. M.eval glm pred.(0) in
-      (*Printf.printf "%.20f\t%.20f\t%b\t%b\n" r0 e0 (r0 = e0) (equal_floats ~d:dx r0 e0)*) 
+      (*Printf.printf "%.20f\t%.20f\t%b\t%b\n" r0 e0 (r0 = e0) (equal_floats ~d:dx r0 e0)*)
       equal_floats ~d:1e-6 r0 e0)
     Spec.([just_postcond_pred is_true]);
 
@@ -152,9 +148,9 @@ let () =
     (fun (pred, _, resp) ->
       let glm = M.regress ~resp pred in
       let m = Descriptive.mean resp in
-      let lambda = Spec (m *. m) in    (* has to be big enough *)
-      let ms = { add_constant_column = false; lambda_spec = Some lambda } in
-      let rdg = M.regress ~spec:ms ~resp pred in
+      let lmd = m *. m in    (* has to be big enough *)
+      let opt = M.opt ~add_constant_column:false ~l2_regularizer:(`S lmd) () in
+      let rdg = M.regress ~opt ~resp pred in
       let rd = Vectors.dot (M.coefficients rdg) (M.coefficients rdg) in
       let gd = Vectors.dot (M.coefficients glm) (M.coefficients glm) in
       rd < gd)
@@ -166,12 +162,12 @@ let () =
     Gen.(general_model 1e11 ~max_samples ~max_predictors)
     (fun (pred, _, resp) ->
       let r,c = Matrices.dim pred in
-      let reg =
+      let tik_matrix =
         Array.init r (fun i -> Array.init c (fun j ->
           if i = j then 1.0 else 0.0))
       in
-      let opt = {regularizer = reg; lambda_spec = None} in
-      let _t  = T.regress ~spec:opt ~resp pred in
+      let opt = T.opt ~tik_matrix () in
+      let _t  = T.regress ~opt ~resp pred in
       true)
     Spec.([just_postcond_pred is_true]);
 
diff --git a/src/lib/util.ml b/src/lib/util.ml
index 613f075..aa56673 100644
--- a/src/lib/util.ml
+++ b/src/lib/util.ml
@@ -192,8 +192,8 @@ end
 
 module type Optional_arg_intf = sig
 
-  type spec             (** type of default argument. *)
-  val default : spec    (** A default value used when not specified.*)
+  type opt            (** type of default argument. *)
+  val default : opt   (** A default value used when not specified.*)
 end
 
 let fst3 (x,_,_) = x
diff --git a/src/lib/util.mli b/src/lib/util.mli
index fbb747a..7803959 100644
--- a/src/lib/util.mli
+++ b/src/lib/util.mli
@@ -172,8 +172,8 @@ end
 (** When passing optional arguments to procedures. *)
 module type Optional_arg_intf = sig
 
-  type spec             (** type of default argument. *)
-  val default : spec    (** A default value used when not specified.*)
+  type opt            (** type of default argument. *)
+  val default : opt   (** A default value used when not specified.*)
 end