diff --git a/theories/collections.v b/theories/collections.v
index 1a34474de8b500c426a104cc83b9d8e12d4ea8d7..e4856b525e9e067dce3da35af50a471c206f77de 100644
--- a/theories/collections.v
+++ b/theories/collections.v
@@ -4,7 +4,8 @@
importantly, it implements some tactics to automatically solve goals involving
collections. *)
From stdpp Require Export orders list.
-Set Default Proof Using "Type*".
+(* FIXME: This file needs a 'Proof Using' hint, but the default we use
+ everywhere makes for lots of extra ssumptions. *)
Instance collection_equiv `{ElemOf A C} : Equiv C := λ X Y,
∀ x, x ∈ X ↔ x ∈ Y.
diff --git a/theories/fin_maps.v b/theories/fin_maps.v
index cc85921f2f41792e5d4c8f6dd0b91d3d968f6764..89b5ebedb3898e4109fddb66e847fbbe3a2bd5f6 100644
--- a/theories/fin_maps.v
+++ b/theories/fin_maps.v
@@ -6,7 +6,8 @@ induction principles for finite maps and implements the tactic
[simplify_map_eq] to simplify goals involving finite maps. *)
From Coq Require Import Permutation.
From stdpp Require Export relations orders vector.
-Set Default Proof Using "Type*".
+(* FIXME: This file needs a 'Proof Using' hint, but the default we use
+ everywhere makes for lots of extra ssumptions. *)
(** * Axiomatization of finite maps *)
(** We require Leibniz equality to be extensional on finite maps. This of