diff --git a/interpreter/spec/valid.ml b/interpreter/spec/valid.ml
index 5642678d8b..495a478b5f 100644
--- a/interpreter/spec/valid.ml
+++ b/interpreter/spec/valid.ml
@@ -365,11 +365,10 @@ let check_data (c : context) (seg : memory_segment) =
   check_const c offset I32Type;
   ignore (memory c index)
 
-let check_global (c : context) (glob : global) : context =
+let check_global (c : context) (glob : global) =
   let {gtype; value} = glob.it in
   let GlobalType (t, mut) = gtype in
-  check_const c value t;
-  {c with globals = c.globals @ [gtype]}
+  check_const c value t
 
 
 (* Modules *)
@@ -413,24 +412,29 @@ let check_export (c : context) (set : NameSet.t) (ex : export) : NameSet.t =
 
 let check_module (m : module_) =
   let
-    {types; imports; tables; memories; globals; funcs; start; elems; data;
-     exports} = m.it in
-  let c = List.fold_right check_import imports {(context m) with types} in
-  let c' =
-    { (List.fold_left check_global c globals) with
-      funcs = c.funcs @ List.map (fun f -> type_ c f.it.ftype) funcs;
-      tables = c.tables @ List.map (fun tab -> tab.it.ttype) tables;
-      memories = c.memories @ List.map (fun mem -> mem.it.mtype) memories;
+    { types; imports; tables; memories; globals; funcs; start; elems; data;
+      exports } = m.it
+  in
+  let c0 = List.fold_right check_import imports {(context m) with types} in
+  let c1 =
+    { c0 with
+      funcs = c0.funcs @ List.map (fun f -> type_ c0 f.it.ftype) funcs;
+      tables = c0.tables @ List.map (fun tab -> tab.it.ttype) tables;
+      memories = c0.memories @ List.map (fun mem -> mem.it.mtype) memories;
     }
   in
-  require (List.length c'.tables <= 1) m.at
+  let c =
+    { c1 with globals = c1.globals @ List.map (fun g -> g.it.gtype) globals }
+  in
+  List.iter (check_global c1) globals;
+  List.iter (check_table c1) tables;
+  List.iter (check_memory c1) memories;
+  List.iter (check_elem c1) elems;
+  List.iter (check_data c1) data;
+  List.iter (check_func c) funcs;
+  check_start c start;
+  ignore (List.fold_left (check_export c) NameSet.empty exports);
+  require (List.length c.tables <= 1) m.at
     "multiple tables are not allowed (yet)";
-  require (List.length c'.memories <= 1) m.at
-    "multiple memories are not allowed (yet)";
-  List.iter (check_func c') funcs;
-  List.iter (check_table c') tables;
-  List.iter (check_memory c') memories;
-  List.iter (check_elem c') elems;
-  List.iter (check_data c') data;
-  ignore (List.fold_left (check_export c') NameSet.empty exports);
-  check_start c' start
+  require (List.length c.memories <= 1) m.at
+    "multiple memories are not allowed (yet)"
diff --git a/interpreter/test/memory.wast b/interpreter/test/memory.wast
index b9fb1bb029..d05b18fac1 100644
--- a/interpreter/test/memory.wast
+++ b/interpreter/test/memory.wast
@@ -10,10 +10,11 @@
 (module (memory 1 2)
   (data (i32.const 0) "a") (data (i32.const 1) "b") (data (i32.const 2) "c")
 )
-(module (memory 1) (global i32 (i32.const 0)) (data (get_global 0) "a"))
-(module (memory 1) (global $g i32 (i32.const 0)) (data (get_global $g) "a"))
-(module (memory 1) (data (get_global 0) "a") (global i32 (i32.const 0)))
-(module (memory 1) (data (get_global $g) "a") (global $g i32 (i32.const 0)))
+(module (global (import "spectest" "global") i32) (memory 1) (data (get_global 0) "a"))
+(module (global $g (import "spectest" "global") i32) (memory 1) (data (get_global $g) "a"))
+;; Use of internal globals in constant expressions is not allowed in MVP.
+;; (module (memory 1) (data (get_global 0) "a") (global i32 (i32.const 0)))
+;; (module (memory 1) (data (get_global $g) "a") (global $g i32 (i32.const 0)))
 
 (module (memory (data)) (func (export "memsize") (result i32) (current_memory)))
 (assert_return (invoke "memsize") (i32.const 0))
@@ -38,10 +39,11 @@
   (module (memory 1) (data (nop)))
   "constant expression required"
 )
-(assert_invalid
-  (module (memory 1) (data (get_global $g)) (global $g (mut i32) (i32.const 0)))
-  "constant expression required"
-)
+;; Use of internal globals in constant expressions is not allowed in MVP.
+;; (assert_invalid
+;;   (module (memory 1) (data (get_global $g)) (global $g (mut i32) (i32.const 0)))
+;;   "constant expression required"
+;; )
 
 (assert_unlinkable
   (module (memory 0 0) (data (i32.const 0) "a"))
@@ -57,7 +59,7 @@
   ""  ;; either out of memory or segment does not fit
 ;)
 (assert_unlinkable
-  (module (memory 1) (data (get_global 0) "a") (global i32 (i32.const 0x10000)))
+  (module (global (import "spectest" "global") i32) (memory 0) (data (get_global 0) "a"))
   "data segment does not fit"
 )