diff --git a/compiler/basicTypes/DataCon.lhs b/compiler/basicTypes/DataCon.lhs
index c82f018962cbbd818b0b999817b65a234f396ab7..edb3627993d28c2732c7085f1e16f00d7400868b 100644
--- a/compiler/basicTypes/DataCon.lhs
+++ b/compiler/basicTypes/DataCon.lhs
@@ -391,6 +391,7 @@ data DataCon
 				-- The actual fixity is stored elsewhere
 
         dcPromoted :: Maybe TyCon    -- The promoted TyCon if this DataCon is promotable
+                                     -- See Note [Promoted data constructors] in TyCon
   }
   deriving Data.Typeable.Typeable
 
@@ -559,9 +560,10 @@ mkDataCon name declared_infix
 	  mkFunTys rep_arg_tys $
 	  mkTyConApp rep_tycon (mkTyVarTys univ_tvs)
 
-    mb_promoted 
-      | is_vanilla   -- No existentials or context
-      , all (isLiftedTypeKind . tyVarKind) univ_tvs
+    mb_promoted   -- See Note [Promoted data constructors] in TyCon
+      | all (isLiftedTypeKind . tyVarKind) (univ_tvs ++ ex_tvs)
+                          -- No kind polymorphism, and all of kind *
+      , null full_theta   -- No constraints
       , all isPromotableType orig_arg_tys
       = Just (mkPromotedDataCon con name (getUnique name) prom_kind arity)
       | otherwise 
diff --git a/compiler/types/TyCon.lhs b/compiler/types/TyCon.lhs
index 5398adc8f1fdea0f519089527926b539b4e682a5..e90cdec24bda743b3821ab32f011d99e79b7f766 100644
--- a/compiler/types/TyCon.lhs
+++ b/compiler/types/TyCon.lhs
@@ -581,8 +581,10 @@ Note [Promoted data constructors]
 A data constructor can be promoted to become a type constructor,
 via the PromotedTyCon alternative in TyCon.
 
-* Only "vanilla" data constructors are promoted; ones with no GADT
-  stuff, no existentials, etc.  We might generalise this later.
+* Only data constructors with  
+     (a) no kind polymorphism
+     (b) no constraints in its type (eg GADTs)
+  are promoted.  Existentials are ok; see Trac #7347.
 
 * The TyCon promoted from a DataCon has the *same* Name and Unique as
   the DataCon.  Eg. If the data constructor Data.Maybe.Just(unique 78,