diff --git a/gmp.c b/gmp.c
index 3422350e..2a6221e6 100644
--- a/gmp.c
+++ b/gmp.c
@@ -723,7 +723,7 @@ richcompare(PyObject *self, PyObject *other, int op)
 fallback:
     Py_RETURN_NOTIMPLEMENTED;
 numbers:
-    self = to_float(self);
+    self = MPZ_to_int((MPZ_Object *)self);
     if (!self) {
         return NULL; /* LCOV_EXCL_LINE */
     }
diff --git a/tests/test_mpz.py b/tests/test_mpz.py
index fad45e7a..893af4ec 100644
--- a/tests/test_mpz.py
+++ b/tests/test_mpz.py
@@ -343,6 +343,7 @@ def test_repr(x):
 
 
 @given(bigints(), floats(allow_nan=False))
+@example(9007199254740993, 9007199254740992.0)
 def test_richcompare_mixed(x, y):
     mx = mpz(x)
     for op in [operator.eq, operator.ne, operator.lt, operator.le,
@@ -357,10 +358,6 @@ def test_richcompare_errors():
         mx > 1j
     with pytest.raises(TypeError):
         mx > object()
-    with pytest.raises(OverflowError):
-        mpz(10**1000) < 1.1
-    with pytest.raises(OverflowError):
-        mpz(10**1000) > 1.1
 
 
 def test_hash_caching():