diff --git a/src/cvc5_mappings.default.ml b/src/cvc5_mappings.default.ml
index 4a53a972..a7c85d69 100644
--- a/src/cvc5_mappings.default.ml
+++ b/src/cvc5_mappings.default.ml
@@ -431,14 +431,19 @@ module Fresh_cvc5 () = struct
   end
 
   module Solver = struct
+    let set_param (type a) slv (param : a Params.param) (v : a) : unit =
+      match param with
+      | Timeout -> Solver.set_option slv "tlimit" (string_of_int v)
+      | Model -> Solver.set_option slv "produce-models" (string_of_bool v)
+      | Unsat_core ->
+        Solver.set_option slv "produce-unsat-core" (string_of_bool v)
+      | Ematching -> Solver.set_option slv "e-matching" (string_of_bool v)
+      | Parallel | Num_threads -> ()
+
     let set_params slv params =
-      Solver.set_option slv "e-matching"
-        (string_of_bool @@ Params.get params Ematching);
-      Solver.set_option slv "tlimit" (string_of_int @@ Params.get params Timeout);
-      Solver.set_option slv "produce-models"
-        (string_of_bool @@ Params.get params Model);
-      Solver.set_option slv "produce-unsat-cores"
-        (string_of_bool @@ Params.get params Unsat_core)
+      List.iter
+        (fun (Params.P (p, v)) -> set_param slv p v)
+        (Params.to_list params)
 
     let make ?params ?logic () =
       let logic = Option.map (fun l -> Fmt.str "%a" Ty.pp_logic l) logic in
diff --git a/src/solvers/params.ml b/src/solvers/params.ml
index 30283f5b..da4a6749 100644
--- a/src/solvers/params.ml
+++ b/src/solvers/params.ml
@@ -24,14 +24,29 @@ type _ param =
   | Parallel : bool param
   | Num_threads : int param
 
-type t =
-  { timeout : int
-  ; model : bool
-  ; unsat_core : bool
-  ; ematching : bool
-  ; parallel : bool
-  ; num_threads : int
-  }
+let discr : type a. a param -> int = function
+  | Timeout -> 0
+  | Model -> 1
+  | Unsat_core -> 2
+  | Ematching -> 3
+  | Parallel -> 4
+  | Num_threads -> 5
+
+module Key = struct
+  type t = K : 'a param -> t
+
+  let v v = K v
+
+  let compare (K a) (K b) = compare (discr a) (discr b)
+end
+
+module Pmap = Map.Make (Key)
+
+type param' = P : 'a param * 'a -> param'
+
+let p k v = P (k, v)
+
+type t = param' Pmap.t
 
 let default_timeout = 2147483647
 
@@ -43,7 +58,6 @@ let default_ematching = true
 
 let default_parallel = false
 
-(* FIXME: Will this be problematic if only (Parallel, true) is specified? *)
 let default_num_threads = 1
 
 let default_value (type a) (param : a param) : a =
@@ -56,22 +70,14 @@ let default_value (type a) (param : a param) : a =
   | Num_threads -> default_num_threads
 
 let default () =
-  { timeout = default_timeout
-  ; model = default_model
-  ; unsat_core = default_unsat_core
-  ; ematching = default_ematching
-  ; parallel = default_parallel
-  ; num_threads = default_num_threads
-  }
+  Pmap.empty
+  |> Pmap.add (Key.v Timeout) (p Timeout default_timeout)
+  |> Pmap.add (Key.v Model) (p Model default_model)
+  |> Pmap.add (Key.v Unsat_core) (p Unsat_core default_unsat_core)
+  |> Pmap.add (Key.v Ematching) (p Ematching default_ematching)
 
 let set (type a) (params : t) (param : a param) (value : a) : t =
-  match param with
-  | Timeout -> { params with timeout = value }
-  | Model -> { params with model = value }
-  | Unsat_core -> { params with unsat_core = value }
-  | Ematching -> { params with ematching = value }
-  | Parallel -> { params with parallel = value }
-  | Num_threads -> { params with num_threads = value }
+  Pmap.add (Key.v param) (p param value) params
 
 let opt (type a) (params : t) (param : a param) (opt_value : a option) : t =
   Option.fold ~none:params ~some:(set params param) opt_value
@@ -80,10 +86,14 @@ let ( $ ) (type a) (params : t) ((param, value) : a param * a) : t =
   set params param value
 
 let get (type a) (params : t) (param : a param) : a =
-  match param with
-  | Timeout -> params.timeout
-  | Model -> params.model
-  | Unsat_core -> params.unsat_core
-  | Ematching -> params.ematching
-  | Parallel -> params.parallel
-  | Num_threads -> params.num_threads
+  match (param, Pmap.find (Key.v param) params) with
+  | Timeout, P (Timeout, v) -> v
+  | Model, P (Model, v) -> v
+  | Unsat_core, P (Unsat_core, v) -> v
+  | Ematching, P (Ematching, v) -> v
+  | Parallel, P (Parallel, v) -> v
+  | Num_threads, P (Num_threads, v) -> v
+  | (Timeout | Model | Unsat_core | Ematching | Parallel | Num_threads), _ ->
+    assert false
+
+let to_list (type a) (params : t) = List.map snd @@ Pmap.bindings params
diff --git a/src/solvers/params.mli b/src/solvers/params.mli
index 2ad81765..2fca0951 100644
--- a/src/solvers/params.mli
+++ b/src/solvers/params.mli
@@ -16,6 +16,8 @@
 (* along with this program.  If not, see <https://www.gnu.org/licenses/>.  *)
 (***************************************************************************)
 
+type t
+
 type _ param =
   | Timeout : int param
     (** Specifies a timeout in miliseconds for each [check] call *)
@@ -26,7 +28,7 @@ type _ param =
   | Num_threads : int param
     (** Speficied the maximum number of threads to use in parallel mode *)
 
-type t
+type param' = P : 'a param * 'a -> param'
 
 val default_value : 'a param -> 'a
 
@@ -43,3 +45,5 @@ val opt : t -> 'a param -> 'a option -> t
 
 (** [get params p] fetches the current value for parameter [p] *)
 val get : t -> 'a param -> 'a
+
+val to_list : t -> param' list
diff --git a/src/z3_mappings.default.ml b/src/z3_mappings.default.ml
index 2cddca64..4fd2094e 100644
--- a/src/z3_mappings.default.ml
+++ b/src/z3_mappings.default.ml
@@ -438,19 +438,19 @@ module M = struct
       in
       List.fold_left add_entry Statistics.Map.empty statistics
 
+    let set_param (type a) (param : a Params.param) (v : a) : unit =
+      match param with
+      | Timeout -> Z3.Params.update_param_value ctx "timeout" (string_of_int v)
+      | Model -> Z3.Params.update_param_value ctx "model" (string_of_bool v)
+      | Unsat_core ->
+        Z3.Params.update_param_value ctx "unsat_core" (string_of_bool v)
+      | Ematching -> Z3.set_global_param "smt.ematching" (string_of_bool v)
+      | Parallel -> Z3.set_global_param "parallel.enable" (string_of_bool v)
+      | Num_threads ->
+        Z3.set_global_param "parallel.threads.max" (string_of_int v)
+
     let set_params (params : Params.t) =
-      Z3.set_global_param "smt.ematching"
-        (string_of_bool @@ Params.get params Ematching);
-      Z3.set_global_param "parallel.enable"
-        (string_of_bool @@ Params.get params Parallel);
-      Z3.set_global_param "parallel.threads.max"
-        (string_of_int @@ Params.get params Num_threads);
-      Z3.Params.update_param_value ctx "timeout"
-        (string_of_int @@ Params.get params Timeout);
-      Z3.Params.update_param_value ctx "model"
-        (string_of_bool @@ Params.get params Model);
-      Z3.Params.update_param_value ctx "unsat_core"
-        (string_of_bool @@ Params.get params Unsat_core)
+      List.iter (fun (Params.P (p, v)) -> set_param p v) (Params.to_list params)
 
     module Solver = struct
       (* TODO: parameters *)
diff --git a/test/solver/test_solver_params.ml b/test/solver/test_solver_params.ml
index 045bf9b8..668de040 100644
--- a/test/solver/test_solver_params.ml
+++ b/test/solver/test_solver_params.ml
@@ -12,8 +12,10 @@ module Make (M : Mappings_intf.S) = struct
 
   let () =
     let params =
-      default () $ (Timeout, 900) $ (Unsat_core, true) $ (Model, false)
-      $ (Ematching, false)
+      default () $ (Timeout, 900) $ (Model, false) $ (Unsat_core, true)
+      $ (Ematching, false) $ (Parallel, true) $ (Num_threads, 1)
     in
-    ignore (Solver.create ~params ())
+    assert (Params.get params Unsat_core);
+    let _ : Solver.t = Solver.create ~params () in
+    ()
 end