diff --git a/src/goto-programs/json_expr.cpp b/src/goto-programs/json_expr.cpp
index 16139131b90..4be5606f613 100644
--- a/src/goto-programs/json_expr.cpp
+++ b/src/goto-programs/json_expr.cpp
@@ -53,7 +53,7 @@ static exprt simplify_json_expr(const exprt &src)
     }
     else if(
       object.id() == ID_index && to_index_expr(object).index().is_constant() &&
-      to_constant_expr(to_index_expr(object).index()).value_is_zero_string())
+      to_constant_expr(to_index_expr(object).index()).is_zero())
     {
       // simplify expressions of the form  &array[0]
       return simplify_json_expr(to_index_expr(object).array());
diff --git a/src/util/simplify_expr_int.cpp b/src/util/simplify_expr_int.cpp
index 2087564a387..a80bf66dc89 100644
--- a/src/util/simplify_expr_int.cpp
+++ b/src/util/simplify_expr_int.cpp
@@ -777,7 +777,7 @@ simplify_exprt::simplify_bitwise(const multi_ary_exprt &expr)
       }
       else if(
         it->is_constant() && it->type().id() == ID_bv &&
-        to_constant_expr(*it).value_is_zero_string() &&
+        *it == to_bv_type(it->type()).all_zeros_expr() &&
         new_expr.operands().size() > 1)
       {
         it = new_expr.operands().erase(it);
diff --git a/src/util/std_expr.h b/src/util/std_expr.h
index d9ca4f64bab..a9cc349741d 100644
--- a/src/util/std_expr.h
+++ b/src/util/std_expr.h
@@ -3005,8 +3005,6 @@ class constant_exprt : public nullary_exprt
     set(ID_value, value);
   }
 
-  bool value_is_zero_string() const;
-
   /// Returns true if \p expr has a pointer type and a value NULL; it also
   /// returns true when \p expr has value zero and NULL_is_zero is true; returns
   /// false in all other cases.
@@ -3023,6 +3021,9 @@ class constant_exprt : public nullary_exprt
   {
     check(expr, vm);
   }
+
+protected:
+  bool value_is_zero_string() const;
 };
 
 template <>
diff --git a/unit/goto-symex/goto_symex_state.cpp b/unit/goto-symex/goto_symex_state.cpp
index 8e5d02395e6..7d76dd61fab 100644
--- a/unit/goto-symex/goto_symex_state.cpp
+++ b/unit/goto-symex/goto_symex_state.cpp
@@ -172,8 +172,7 @@ SCENARIO(
           const symbol_exprt object_symbol =
             to_symbol_expr(object_descriptor->object());
           REQUIRE(object_symbol.get_identifier() == "int_value!0");
-          REQUIRE(to_constant_expr(object_descriptor->offset())
-                    .value_is_zero_string());
+          REQUIRE(to_constant_expr(object_descriptor->offset()).is_zero());
         }
         THEN("The target equations are unchanged")
         {