diff --git a/conservancy_beancount/reports/core.py b/conservancy_beancount/reports/core.py
index 72ade4db951079379bae5b8ccb5977cbc558a4d7..2c5aaf5096ad2f205e97e29f81276bd155c3aa47 100644
--- a/conservancy_beancount/reports/core.py
+++ b/conservancy_beancount/reports/core.py
@@ -80,10 +80,17 @@ class Balance(Mapping[str, data.Amount]):
     Each key is a Beancount currency string, and each value represents the
     balance in that currency.
     """
-    __slots__ = ('_currency_map',)
+    __slots__ = ('_currency_map', 'tolerance')
+    TOLERANCE = Decimal('0.01')
 
-    def __init__(self, source: Iterable[data.Amount]=()) -> None:
+    def __init__(self,
+                 source: Iterable[data.Amount]=(),
+                 tolerance: Optional[Decimal]=None,
+    ) -> None:
+        if tolerance is None:
+            tolerance = self.TOLERANCE
         self._currency_map = {amount.currency: amount for amount in source}
+        self.tolerance = tolerance
 
     def _add_amount(self,
                     currency_map: MutableMapping[str, data.Amount],
@@ -147,19 +154,24 @@ class Balance(Mapping[str, data.Amount]):
     ) -> bool:
         return all(op_func(amt.number, operand) for amt in self.values())
 
+    @staticmethod
+    def within_tolerance(dec: DecimalCompat, tolerance: DecimalCompat) -> bool:
+        dec = cast(Decimal, dec)
+        return abs(dec) < tolerance
+
     def eq_zero(self) -> bool:
-        """Returns true if all amounts in the balance == 0."""
-        return self._all_amounts(operator.eq, 0)
+        """Returns true if all amounts in the balance == 0, within tolerance."""
+        return self._all_amounts(self.within_tolerance, self.tolerance)
 
     is_zero = eq_zero
 
     def ge_zero(self) -> bool:
-        """Returns true if all amounts in the balance >= 0."""
-        return self._all_amounts(operator.ge, 0)
+        """Returns true if all amounts in the balance >= 0, within tolerance."""
+        return self._all_amounts(operator.ge, -self.tolerance)
 
     def le_zero(self) -> bool:
-        """Returns true if all amounts in the balance <= 0."""
-        return self._all_amounts(operator.le, 0)
+        """Returns true if all amounts in the balance <= 0, within tolerance."""
+        return self._all_amounts(operator.le, self.tolerance)
 
     def format(self,
                fmt: Optional[str]='#,#00.00 ¤¤',
diff --git a/tests/test_reports_balance.py b/tests/test_reports_balance.py
index d827018f52d459839657bda2acf7a5b7bd93b473..8ab0a587b9cd9eb7089af14fcfd544200009a73d 100644
--- a/tests/test_reports_balance.py
+++ b/tests/test_reports_balance.py
@@ -92,6 +92,8 @@ def test_mixed_balance():
     ({'JPY': 10}, False),
     ({'JPY': 10, 'BRL': 0}, False),
     ({'JPY': 10, 'BRL': 20}, False),
+    ({'USD': '0.00015'}, True),
+    ({'EUR': '-0.00052'}, True),
 ])
 def test_eq_zero(mapping, expected):
     balance = core.Balance(amounts_from_map(mapping))
@@ -108,6 +110,8 @@ def test_eq_zero(mapping, expected):
     ({'JPY': 10}, True),
     ({'JPY': 10, 'BRL': 0}, True),
     ({'JPY': 10, 'BRL': 20}, True),
+    ({'USD': '0.00015'}, True),
+    ({'EUR': '-0.00052'}, True),
 ])
 def test_ge_zero(mapping, expected):
     balance = core.Balance(amounts_from_map(mapping))
@@ -123,6 +127,8 @@ def test_ge_zero(mapping, expected):
     ({'JPY': 10}, False),
     ({'JPY': 10, 'BRL': 0}, False),
     ({'JPY': 10, 'BRL': 20}, False),
+    ({'USD': '0.00015'}, True),
+    ({'EUR': '-0.00052'}, True),
 ])
 def test_le_zero(mapping, expected):
     balance = core.Balance(amounts_from_map(mapping))