diff --git a/ml-proto/spec/check.ml b/ml-proto/spec/check.ml
index a64b88f7df..abef23d65b 100644
--- a/ml-proto/spec/check.ml
+++ b/ml-proto/spec/check.ml
@@ -256,7 +256,8 @@ and check_has_memory c at =
 and check_memop memop at =
   require (memop.offset >= 0L) at "negative offset";
   require (memop.offset <= 0xffffffffL) at "offset too large";
-  require (Lib.Int.is_power_of_two memop.align) at "non-power-of-two alignment";
+  require (Lib.Int.is_power_of_two memop.align) at "alignment must be a power of two";
+  require (memop.align <= size memop.ty) at "alignment must not be larger than natural"
 
 and check_mem_type ty sz at =
   require (ty = Int64Type || sz <> Memory.Mem32) at "memory size too big"
diff --git a/ml-proto/spec/types.ml b/ml-proto/spec/types.ml
index 5081be252d..a5ac41d446 100644
--- a/ml-proto/spec/types.ml
+++ b/ml-proto/spec/types.ml
@@ -4,6 +4,14 @@ type value_type = Int32Type | Int64Type | Float32Type | Float64Type
 type expr_type = value_type option
 type func_type = {ins : value_type list; out : expr_type}
 
+
+(* Attributes *)
+
+let size = function
+  | Int32Type | Float32Type -> 4
+  | Int64Type | Float64Type -> 8
+
+
 (* String conversion *)
 
 let string_of_value_type = function
diff --git a/ml-proto/test/memory.wast b/ml-proto/test/memory.wast
index 390717e4cd..def709ba25 100644
--- a/ml-proto/test/memory.wast
+++ b/ml-proto/test/memory.wast
@@ -48,28 +48,41 @@
 ;; Test alignment annotation rules
 (module (memory 0) (func (i32.load8_u align=2 (i32.const 0))))
 (module (memory 0) (func (i32.load16_u align=4 (i32.const 0))))
-(module (memory 0) (func (i32.load align=8 (i32.const 0))))
-(module (memory 0) (func (f32.load align=8 (i32.const 0))))
+(module (memory 0) (func (i32.load align=4 (i32.const 0))))
+(module (memory 0) (func (f32.load align=4 (i32.const 0))))
 
 (assert_invalid
   (module (memory 0) (func (i64.load align=0 (i32.const 0))))
-  "non-power-of-two alignment"
+  "alignment must be a power of two"
 )
 (assert_invalid
   (module (memory 0) (func (i64.load align=3 (i32.const 0))))
-  "non-power-of-two alignment"
+  "alignment must be a power of two"
 )
 (assert_invalid
   (module (memory 0) (func (i64.load align=5 (i32.const 0))))
-  "non-power-of-two alignment"
+  "alignment must be a power of two"
 )
 (assert_invalid
   (module (memory 0) (func (i64.load align=6 (i32.const 0))))
-  "non-power-of-two alignment"
+  "alignment must be a power of two"
 )
 (assert_invalid
   (module (memory 0) (func (i64.load align=7 (i32.const 0))))
-  "non-power-of-two alignment"
+  "alignment must be a power of two"
+)
+
+(assert_invalid
+  (module (memory 0) (func (i64.load align=16 (i32.const 0))))
+  "alignment must not be larger than natural"
+)
+(assert_invalid
+  (module (memory 0) (func (i64.load align=32 (i32.const 0))))
+  "alignment must not be larger than natural"
+)
+(assert_invalid
+  (module (memory 0) (func (i32.load align=8 (i32.const 0))))
+  "alignment must not be larger than natural"
 )
 
 (module