diff --git a/src/lib/frontend/models.ml b/src/lib/frontend/models.ml
index 0cdc01935..0849ff6c8 100644
--- a/src/lib/frontend/models.ml
+++ b/src/lib/frontend/models.ml
@@ -481,6 +481,11 @@ let pp_constant ppf (_, t) =
   Format.fprintf ppf "%a" SmtlibCounterExample.pp_dummy_value_of_type t
 
 let output_concrete_model fmt props ~functions ~constants ~arrays =
+  if ModelMap.(is_suspicious functions || is_suspicious constants
+               || is_suspicious arrays) then
+    Format.fprintf fmt "; This model is a best-effort. It includes symbols
+        for which model generation is known to be incomplete. @.";
+
   Format.fprintf fmt "@[<v 2>(";
   if Options.get_model_type_constraints () then
     begin
diff --git a/src/lib/structures/modelMap.ml b/src/lib/structures/modelMap.ml
index 10d60ffe8..ff06afff0 100644
--- a/src/lib/structures/modelMap.ml
+++ b/src/lib/structures/modelMap.ml
@@ -80,24 +80,50 @@ module V = Set.Make
 
 type key = P.key
 type elt = V.t
-type t = V.t P.t
 
-let add p v mp =
-  let prof_p = try P.find p mp with Not_found -> V.empty in
-  if V.mem v prof_p then mp
-  else P.add p (V.add v prof_p) mp
+type t = {
+  values : V.t P.t;
+  suspicious : bool;
+}
 
-let iter f =
+let is_suspicious_name hs =
+  match Hstring.view hs with
+  | "@/" | "@%" | "@*" -> true
+  | _ -> false
+
+(* The model generation is known to be imcomplete for FPA and Bitvector
+   theories. *)
+let is_suspicious_symbol = function
+  | Sy.Op (Float | Fixed | Abs_int | Abs_real | Sqrt_real
+          | Sqrt_real_default | Sqrt_real_excess
+          | Real_of_int | Int_floor | Int_ceil
+          | Max_int | Max_real | Min_int | Min_real
+          | Pow | Integer_log2 | Int2BV _ | BV2Nat
+          | BVand | BVor | Integer_round) -> true
+  | Sy.Name (hs, _, _) when is_suspicious_name hs -> true
+  | _ -> false
+
+let add ((sy, _, _) as p) v { values; suspicious } =
+  let prof_p = try P.find p values with Not_found -> V.empty in
+  let values =
+    if V.mem v prof_p then values
+    else P.add p (V.add v prof_p) values
+  in
+  { values; suspicious = suspicious || is_suspicious_symbol sy }
+
+let iter f { values; _ } =
   P.iter (fun ((sy, _, _) as key) value ->
       match sy with
       | Sy.Name (_, _, true) ->
         (* We don't print constants defined by the user. *)
         ()
       | _ -> f key value
-    )
+    ) values
+
+let[@inline always] is_suspicious { suspicious; _ } = suspicious
 
-let fold = P.fold
+let fold f { values; _ } acc = P.fold f values acc
 
-let empty = P.empty
+let empty = { values = P.empty; suspicious = false }
 
-let is_empty = P.is_empty
+let is_empty { values; _ } = P.is_empty values
diff --git a/src/lib/structures/modelMap.mli b/src/lib/structures/modelMap.mli
index 87cf34bba..c9584a88e 100644
--- a/src/lib/structures/modelMap.mli
+++ b/src/lib/structures/modelMap.mli
@@ -42,7 +42,8 @@ module V : Set.S with type elt =
 
 type key = P.key
 type elt = V.t
-type t = V.t P.t
+
+type t
 
 val add : key -> V.elt -> t -> t
 
@@ -53,3 +54,7 @@ val fold : (key -> elt -> 'acc -> 'acc) -> t -> 'acc -> 'acc
 val empty : t
 
 val is_empty : t -> bool
+
+val is_suspicious : t -> bool
+(* Determine if the model is suspicious as it contains symbols
+   of theories for which the model generation is not properly supported. *)