diff --git a/millify/__init__.py b/millify/__init__.py
index ed58dfa..51c5f0e 100644
--- a/millify/__init__.py
+++ b/millify/__init__.py
@@ -23,6 +23,13 @@ def millify(n, precision=0, drop_nulls=True, prefixes=[]):
     millidx = max(0, min(len(millnames) - 1,
                          int(math.floor(0 if n == 0 else math.log10(abs(n)) / 3))))
     result = '{:.{precision}f}'.format(n / 10**(3 * millidx), precision=precision)
+    # Rounding to ``precision`` digits can push the mantissa up to 1000
+    # (e.g. 999999 -> "1000k"); carry it into the next unit so the result
+    # stays below 1000 ("1M") while a larger suffix is available.
+    if abs(float(result)) >= 1000 and millidx < len(millnames) - 1:
+        millidx += 1
+        result = '{:.{precision}f}'.format(n / 10**(3 * millidx),
+                                           precision=precision)
     if drop_nulls:
         result = remove_exponent(Decimal(result))
     return '{0}{dx}'.format(result, dx=millnames[millidx])
diff --git a/test_millify.py b/test_millify.py
new file mode 100644
index 0000000..58f3b4d
--- /dev/null
+++ b/test_millify.py
@@ -0,0 +1,32 @@
+"""Tests for millify()."""
+import pytest
+
+from millify import millify
+
+
+@pytest.mark.parametrize(
+    "n, kwargs, expected",
+    [
+        (0, {}, "0"),
+        (999, {}, "999"),
+        (1000, {}, "1k"),
+        (1000000, {}, "1M"),
+        (1234567, {"precision": 2}, "1.23M"),
+        (-1500, {"precision": 1}, "-1.5k"),
+        # Rounding must carry into the next unit instead of producing
+        # an out-of-range mantissa like "1000k".
+        (999999, {}, "1M"),
+        (999500, {}, "1M"),
+        (999999, {"precision": 2}, "1M"),
+        (-999999, {}, "-1M"),
+        (999999999, {}, "1B"),
+    ],
+)
+def test_millify(n, kwargs, expected):
+    assert millify(n, **kwargs) == expected
+
+
+def test_millify_no_overflow_at_largest_unit():
+    # No larger suffix than "Y" exists, so the mantissa is left as-is
+    # rather than carrying past the table.
+    assert millify(10 ** 27, precision=0).endswith("Y")