diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index 38a17ce..29f7756 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -1468,6 +1468,20 @@ def test_from_hex(self):
         self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS)
         self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS)
 
+        # Regression test for a corner-case bug reported in b.p.o. 44954
+        self.identical(fromHex('0x.8p-1074'), 0.0)
+        self.identical(fromHex('0x.80p-1074'), 0.0)
+        self.identical(fromHex('0x.81p-1074'), TINY)
+        self.identical(fromHex('0x8p-1078'), 0.0)
+        self.identical(fromHex('0x8.0p-1078'), 0.0)
+        self.identical(fromHex('0x8.1p-1078'), TINY)
+        self.identical(fromHex('0x80p-1082'), 0.0)
+        self.identical(fromHex('0x81p-1082'), TINY)
+        self.identical(fromHex('.8p-1074'), 0.0)
+        self.identical(fromHex('8p-1078'), 0.0)
+        self.identical(fromHex('-.8p-1074'), -0.0)
+        self.identical(fromHex('+8p-1078'), 0.0)
+
     def test_roundtrip(self):
         def roundtrip(x):
             return fromHex(toHex(x))