diff --git a/src/include/migraphx/output_iterator.hpp b/src/include/migraphx/output_iterator.hpp
index 7aced4a08a3..e4d670b8537 100644
--- a/src/include/migraphx/output_iterator.hpp
+++ b/src/include/migraphx/output_iterator.hpp
@@ -72,6 +72,12 @@ auto join_back_inserter(Container& c)
         [&](const auto& r) { c.insert(c.end(), r.begin(), r.end()); });
 }
 
+template <class Container>
+auto push_inserter(Container& c)
+{
+    return make_function_output_iterator([&](const auto& x) { c.push(x); });
+}
 } // namespace MIGRAPHX_INLINE_NS
 } // namespace migraphx
+
 #endif // MIGRAPHX_GUARD_MIGRAPHX_OUTPUT_ITERATOR_HPP
diff --git a/src/instruction.cpp b/src/instruction.cpp
index 47bea70379e..219c75e3432 100644
--- a/src/instruction.cpp
+++ b/src/instruction.cpp
@@ -26,7 +26,8 @@
 #include <migraphx/erase.hpp>
 #include <migraphx/module.hpp>
 #include <migraphx/ranges.hpp>
-#include <deque>
+#include <migraphx/output_iterator.hpp>
+#include <queue>
 
 namespace migraphx {
 inline namespace MIGRAPHX_INLINE_NS {
@@ -58,22 +59,39 @@ instruction::instruction(literal l)
 {
 }
 
+struct replace_shape_order
+{
+    instruction_ref start;
+
+    std::size_t location(instruction_ref x) const { return std::distance(start, x); }
+
+    bool operator()(instruction_ref x, instruction_ref y) const
+    {
+        return location(x) > location(y);
+    }
+};
+
 void instruction::replace(const shape& r)
 {
     if(r != result)
     {
         result = r;
-        std::deque<instruction_ref> q(output.begin(), output.end());
+        auto start = std::find_if(output.front()->inputs().begin(),
+                                  output.front()->inputs().end(),
+                                  [&](instruction_ref x) { return this == as_address(x); });
+        assert(as_address(*start) == this);
+        std::priority_queue<instruction_ref, std::vector<instruction_ref>, replace_shape_order> q(
+            output.begin(), output.end(), replace_shape_order{*start});
         while(not q.empty())
         {
-            instruction_ref ins = q.front();
-            q.pop_front();
+            instruction_ref ins = q.top();
+            q.pop();
             assert(ins->name() == "@return" or ins->name().front() != '@');
             shape new_r = compute_shape(ins->op, ins->arguments, ins->module_args);
             if(new_r != ins->result)
             {
                 ins->result = new_r;
-                std::copy(ins->output.begin(), ins->output.end(), std::back_inserter(q));
+                std::copy(ins->output.begin(), ins->output.end(), migraphx::push_inserter(q));
             }
         }
     }
diff --git a/test/instruction.cpp b/test/instruction.cpp
index 134658e336b..0ee22e13553 100644
--- a/test/instruction.cpp
+++ b/test/instruction.cpp
@@ -67,4 +67,24 @@ TEST_CASE(check_replace_shape)
     EXPECT(add->get_shape() == r);
 }
 
+TEST_CASE(check_replace_dag)
+{
+    migraphx::module m;
+    migraphx::shape s{migraphx::shape::float_type, {3, 2}};
+    auto input  = m.add_parameter("x", s);
+    auto reduce = m.add_instruction(migraphx::make_op("reduce_sum", {{"axes", {0}}}), input);
+    auto abs    = m.add_instruction(migraphx::make_op("abs"), reduce);
+    auto sin    = m.add_instruction(migraphx::make_op("sin"), reduce);
+    auto add    = m.add_instruction(migraphx::make_op("add"), abs, sin);
+    auto add2   = m.add_instruction(migraphx::make_op("add"), add, reduce);
+
+    reduce->replace(migraphx::make_op("reduce_sum", {{"axes", {1}}}));
+
+    migraphx::shape r{migraphx::shape::float_type, {3, 1}};
+    EXPECT(reduce->get_shape() == r);
+    EXPECT(abs->get_shape() == r);
+    EXPECT(sin->get_shape() == r);
+    EXPECT(add->get_shape() == r);
+    EXPECT(add2->get_shape() == r);
+}
 int main(int argc, const char* argv[]) { test::run(argc, argv); }