diff --git a/bitcoin/bloom.py b/bitcoin/bloom.py
index d0e3b765..7dfa16a8 100644
--- a/bitcoin/bloom.py
+++ b/bitcoin/bloom.py
@@ -107,8 +107,9 @@ def __init__(self, nElements, nFPRate, nTweak, nFlags):
         """
         LN2SQUARED = 0.4804530139182014246671025263266649717305529515945455
         LN2 = 0.6931471805599453094172321214581765680755001343602552
-        self.vData = bytearray(int(min(-1  / LN2SQUARED * nElements * math.log(nFPRate), self.MAX_BLOOM_FILTER_SIZE * 8) / 8))
-        self.nHashFuncs = int(min(len(self.vData) * 8 / nElements * LN2, self.MAX_HASH_FUNCS))
+        # Rounding must not produce a filter that matches every element.
+        self.vData = bytearray(max(1, int(min(-1  / LN2SQUARED * nElements * math.log(nFPRate), self.MAX_BLOOM_FILTER_SIZE * 8) / 8)))
+        self.nHashFuncs = max(1, int(min(len(self.vData) * 8 / nElements * LN2, self.MAX_HASH_FUNCS)))
         self.nTweak = nTweak
         self.nFlags = nFlags
 
diff --git a/bitcoin/tests/test_bloom.py b/bitcoin/tests/test_bloom.py
index 436a97ea..6cad37f6 100644
--- a/bitcoin/tests/test_bloom.py
+++ b/bitcoin/tests/test_bloom.py
@@ -40,6 +40,20 @@ def T(expected, seed, data):
 
 
 class Test_CBloomFilter(unittest.TestCase):
+    def test_small_and_high_false_positive_rate_filters(self):
+        for elements in (1, 2, 10, 100):
+            for rate in (0.05, 0.1, 0.5, 0.9, 0.9999):
+                filter = CBloomFilter(elements, rate, 0, CBloomFilter.UPDATE_ALL)
+                # An empty filter must not match everything, even when its
+                # calculated storage size or hash count rounds down to zero.
+                self.assertFalse(filter.contains(b'not inserted'))
+                filter.insert(b'inserted')
+                self.assertTrue(filter.contains(b'inserted'))
+                self.assertTrue(filter.IsWithinSizeConstraints())
+                restored = CBloomFilter.deserialize(filter.serialize())
+                self.assertTrue(restored.contains(b'inserted'))
+                self.assertEqual(restored.serialize(), filter.serialize())
+
     def test_create_insert_serialize(self):
         filter = CBloomFilter(3, 0.01, 0, CBloomFilter.UPDATE_ALL)