diff --git a/conservancy_beancount/reports/core.py b/conservancy_beancount/reports/core.py
index 6b2845c..6b759d8 100644
--- a/conservancy_beancount/reports/core.py
+++ b/conservancy_beancount/reports/core.py
@@ -198,17 +198,18 @@ class Balance(Mapping[str, data.Amount]):
                fmt: Optional[str]='#,#00.00 ¤¤',
                sep: str=', ',
                empty: str="Zero balance",
+               tolerance: Optional[Decimal]=None,
     ) -> str:
         """Formats the balance as a string with the given parameters
 
-        If the balance is zero, returns ``empty``. Otherwise, returns a string
-        with each amount in the balance formatted as ``fmt``, separated by
-        ``sep``.
+        If the balance is zero (within tolerance), returns ``empty``.
+        Otherwise, returns a string with each amount in the balance formatted
+        as ``fmt``, separated by ``sep``.
 
         If you set ``fmt`` to None, amounts will be formatted according to the
         user's locale. The default format is Beancount's input format.
         """
-        amounts = [amount for amount in self.values() if amount.number]
+        amounts = list(self.clean_copy(tolerance).values())
         if not amounts:
             return empty
         amounts.sort(key=lambda amt: abs(amt.number), reverse=True)
diff --git a/tests/test_reports_balance.py b/tests/test_reports_balance.py
index 706531e..be5b265 100644
--- a/tests/test_reports_balance.py
+++ b/tests/test_reports_balance.py
@@ -32,6 +32,8 @@ DEFAULT_STRINGS = [
     ({'USD': '20.00'}, "20.00 USD"),
     ({'EUR': '50.00', 'GBP': '80.00'}, "80.00 GBP, 50.00 EUR"),
     ({'JPY': '-5500.00', 'BRL': '-8500.00'}, "-8,500.00 BRL, -5,500 JPY"),
+    ({'USD': 10, 'EUR': '.00015'}, "10.00 USD"),
+    ({'JPY': '-.00015'}, "Zero balance"),
 ]
 
 TOLERANCES = [Decimal(n) for n in ['.1', '.01', '.001', 0]]
@@ -379,3 +381,21 @@ def test_format_none():
 def test_format_empty(empty):
     balance = core.Balance()
     assert balance.format(empty=empty) == empty
+
+@pytest.mark.parametrize('tolerance', TOLERANCES)
+def test_str_tolerance(tolerance):
+    chf = testutil.Amount('.005', 'CHF')
+    actual = str(core.Balance([chf], tolerance))
+    if tolerance > chf.number:
+        assert actual == "Zero balance"
+    else:
+        assert actual == "00.00 CHF"
+
+@pytest.mark.parametrize('tolerance', TOLERANCES)
+def test_format_tolerance(tolerance):
+    chf = testutil.Amount('.005', 'CHF')
+    actual = core.Balance([chf]).format(tolerance=tolerance)
+    if tolerance > chf.number:
+        assert actual == "Zero balance"
+    else:
+        assert actual == "00.00 CHF"