diff --git a/Modules/cPickle.c b/Modules/cPickle.c
index 7f836c3..fb13ba1 100644
--- a/Modules/cPickle.c
+++ b/Modules/cPickle.c
@@ -3465,7 +3465,8 @@
 	errno = 0;
 	d = PyOS_ascii_strtod(s, &endptr);
 
-	if (errno || (endptr[0] != '\n') || (endptr[1] != '\0')) {
+	if ((errno == ERANGE && !(fabs(d) <= 1.0)) ||
+	    (endptr[0] != '\n') || (endptr[1] != '\0')) {
 		PyErr_SetString(PyExc_ValueError,
 				"could not convert string to float");
 		goto finally;