diff --git a/gcc/ada/ChangeLog b/gcc/ada/ChangeLog
index 1f59c88303b1..33d2a1499d4a 100644
--- a/gcc/ada/ChangeLog
+++ b/gcc/ada/ChangeLog
@@ -1,3 +1,14 @@
+2018-12-11  Ed Schonberg  <schonberg@adacore.com>
+
+	* exp_unst.adb (Needs_Fat_Pointer): A fat pointer is required if
+	the entity has a private type whose full view is an
+	unconstrained array type.
+	(Rewrite_One_Ref): If the reference is to a static constant, use
+	its value rather than create a reference through the activation
+	record. This is more efficient, and furthermore indispensable if
+	the context requires a static constant, such as in a branch of a
+	case statement.
+
 2018-12-11  Ed Schonberg  <schonberg@adacore.com>
 
 	* sem_ch3.adb (Analyze_Object_Declaration): Apply
diff --git a/gcc/ada/exp_unst.adb b/gcc/ada/exp_unst.adb
index 882866e38e0c..57b2a9e190c6 100644
--- a/gcc/ada/exp_unst.adb
+++ b/gcc/ada/exp_unst.adb
@@ -246,10 +246,19 @@ package body Exp_Unst is
    -----------------------
 
    function Needs_Fat_Pointer (E : Entity_Id) return Boolean is
+      Typ : Entity_Id;
    begin
-      return Is_Formal (E)
-        and then Is_Array_Type (Etype (E))
-        and then not Is_Constrained (Etype (E));
+      if Is_Formal (E) then
+         Typ := Etype (E);
+         if Is_Private_Type (Typ) and then Present (Full_View (Typ)) then
+            Typ := Full_View (Typ);
+         end if;
+
+         return Is_Array_Type (Typ)
+           and then not Is_Constrained (Typ);
+      else
+         return False;
+      end if;
    end Needs_Fat_Pointer;
 
    ----------------
@@ -2168,6 +2177,21 @@ package body Exp_Unst is
                   goto Continue;
                end if;
 
+               --  If this is a reference to a global constant, use its value
+               --  rather than create a reference. It is more efficient and
+               --  furthermore indispensable if the context requires a
+               --  constant, such as a branch of a case statement.
+
+               if Ekind (UPJ.Ent) = E_Constant
+                 and then Is_True_Constant (UPJ.Ent)
+                 and then Present (Constant_Value (UPJ.Ent))
+                 and then Is_Static_Expression (Constant_Value (UPJ.Ent))
+               then
+                  Rewrite (UPJ.Ref,
+                    New_Copy_Tree (Constant_Value (UPJ.Ent)));
+                  goto Continue;
+               end if;
+
                --  Push the current scope, so that the pointer type Tnn, and
                --  any subsidiary entities resulting from the analysis of the
                --  rewritten reference, go in the right entity chain.