diff --git a/loopy/tools.py b/loopy/tools.py
index e9f9932b7..a4fa95e8a 100644
--- a/loopy/tools.py
+++ b/loopy/tools.py
@@ -73,13 +73,17 @@ class LoopyKeyBuilder(KeyBuilderBase):
     update_for_dict = KeyBuilderBase.update_for_constantdict
     update_for_defaultdict = KeyBuilderBase.update_for_constantdict
 
-    def update_for_BasicSet(self, key_hash, key):  # noqa
-        from islpy import Printer
-        prn = Printer.to_str(key.get_ctx())
-        getattr(prn, "print_"+key._base_name)(key)
-        key_hash.update(prn.get_str().encode("utf8"))
+    def update_for_BasicSet(self, key_hash, key):  # noqa: N802
+        key_hash.update(str(type(key)).encode("utf-8"))
+        self.rec(key_hash, frozenset(key.get_var_dict().keys()))
 
-    def update_for_Map(self, key_hash, key):  # noqa
+        constraints = set()
+        for constraint in key.get_constraints():
+            constraints.add(str(constraint).partition("->")[-1])
+
+        self.rec(key_hash, frozenset(constraints))
+
+    def update_for_Map(self, key_hash, key):  # noqa: N802
         if isinstance(key, isl.Map):
             self.update_for_BasicSet(key_hash, key)
         else:
diff --git a/test/test_misc.py b/test/test_misc.py
index 79c7698e7..9b7a04cbc 100644
--- a/test/test_misc.py
+++ b/test/test_misc.py
@@ -338,6 +338,31 @@ def test_memoize_on_disk_with_pym_expr():
     assert cached_result == uncached_result
 
 
+def test_basicset_keybuilder():
+    # See https://github.com/inducer/loopy/issues/912 for context
+    import islpy as isl
+
+    # Both sets have the same variables and constraints, but in different order.
+    # These sets are generated in test_convolution() in test_apps.py
+    a = isl.BasicSet("[im_w, im_h, nimgs, nfeats] -> "
+                     "{  : im_w >= 7 and im_h >= 7 and nimgs >= 0 and nfeats > 0 }")
+
+    b = isl.BasicSet("[nfeats, nimgs, im_h, im_w] -> "
+                     "{  : nfeats > 0 and nimgs >= 0 and im_h >= 7 and im_w >= 7 }")
+
+    from loopy.tools import LoopyKeyBuilder
+
+    # Equality
+    assert a == b
+    assert a.is_equal(b)
+    assert not a.plain_is_equal(b)
+
+    # Hashing
+    assert hash(a) != hash(b)
+    assert a.get_hash() != b.get_hash()
+    assert LoopyKeyBuilder()(a) == LoopyKeyBuilder()(b)
+
+
 if __name__ == "__main__":
     import sys
     if len(sys.argv) > 1: