diff --git a/rpython/jit/metainterp/optimizeopt/intrelational.py b/rpython/jit/metainterp/optimizeopt/intrelational.py
index 88fc1b7b7ec..1a24b49cad4 100644
--- a/rpython/jit/metainterp/optimizeopt/intrelational.py
+++ b/rpython/jit/metainterp/optimizeopt/intrelational.py
@@ -1,12 +1,44 @@
 from rpython.jit.metainterp.optimize import InvalidLoop
-
+from rpython.jit.metainterp.optimizeopt.intutils import IntBound
 
 class IntOrderInfo(object):
 
-    def __init__(self):
+    def __init__(self, bounds=None):
+        if bounds is None:
+            bounds = IntBound.unbounded()
+        self.bounds = bounds
         self.relations = []
 
+
     def contains(self, concrete_values):
+        if isinstance(concrete_values, dict):
+            return self._contains(concrete_values)
+        else:
+            # assume that `default_values` is a single integer
+            return self.bounds.contains(concrete_values)
+
+    def make_lt(self, other):
+        self.bounds.make_lt(other.bounds)
+        self._make_lt(other)
+
+    def known_lt(self, other):
+        # ask bounds first, as it is cheaper
+        return self.bounds.known_lt(other.bounds) \
+            or self._known_lt(other)
+
+    def abstract_add_const(self, const):
+        bound_other = IntBound.from_constant(const)
+        bounds = self.bounds.add_bound(bound_other)
+        res = IntOrderInfo(bounds)
+        if self.bounds.add_bound_cannot_overflow(bound_other):
+            if const > 0:
+                self.make_lt(res)
+            elif const < 0:
+                res.make_lt(self)
+        return res
+
+
+    def _contains(self, concrete_values):
         # concrete_values: dict[IntOrderInfo, int]
         for order, value in concrete_values.iteritems():
             for relation in order.relations:
@@ -16,14 +48,14 @@ def contains(self, concrete_values):
                     return False
         return True
 
-    def make_lt(self, other):
+    def _make_lt(self, other):
         if other.known_lt(self):
             raise InvalidLoop("Invalid relations: self < other < self")
         if self.known_lt(other):
             return
         self.relations.append(Bigger(other))
 
-    def known_lt(self, other):
+    def _known_lt(self, other):
         todo = self.relations[:]
         seen = dict()
         while todo:
diff --git a/rpython/jit/metainterp/optimizeopt/test/test_intrelational.py b/rpython/jit/metainterp/optimizeopt/test/test_intrelational.py
index 47c42ada659..d3c0350a719 100644
--- a/rpython/jit/metainterp/optimizeopt/test/test_intrelational.py
+++ b/rpython/jit/metainterp/optimizeopt/test/test_intrelational.py
@@ -1,5 +1,6 @@
 import pytest
 from rpython.jit.metainterp.optimizeopt.intrelational import IntOrderInfo
+from rpython.jit.metainterp.optimizeopt.intutils import IntBound
 from rpython.jit.metainterp.optimize import InvalidLoop
 
 
@@ -49,5 +50,14 @@ def test_lt_raises_invalidloop():
     a = IntOrderInfo()
     b = IntOrderInfo()
     a.make_lt(b)
-    with pytest.raises(InvalidLoop) as e:
+    with pytest.raises(InvalidLoop):
         b.make_lt(a)
+
+def test_abstract_add():
+    a = IntOrderInfo()
+    b = a.abstract_add_const(1)
+    assert not a.known_lt(b) # could have overflowed
+
+    a = IntOrderInfo(IntBound(0, 10))
+    b = a.abstract_add_const(1)
+    assert a.known_lt(b) # no overflow