diff --git a/billing/totals.py b/billing/totals.py
--- a/billing/totals.py
+++ b/billing/totals.py
@@ -1,13 +1,13 @@
-from decimal import Decimal, ROUND_HALF_EVEN
+from decimal import Decimal, ROUND_HALF_UP

-ROUNDING = ROUND_HALF_EVEN
+ROUNDING = ROUND_HALF_UP
 CENT = Decimal("0.01")


 def invoice_total(lines, tax_rate):
-    subtotal = sum(Decimal(str(l.qty)) * l.unit_price for l in lines)
-    tax = (subtotal * tax_rate).quantize(CENT, rounding=ROUNDING)
-    return (subtotal + tax).quantize(CENT, rounding=ROUNDING)
+    subtotal = sum((Decimal(str(l.qty)) * l.unit_price).quantize(CENT, rounding=ROUNDING) for l in lines)
+    tax = (subtotal * tax_rate).quantize(CENT, rounding=ROUNDING)
+    return subtotal + tax
diff --git a/tests/billing/test_totals.py b/tests/billing/test_totals.py
--- a/tests/billing/test_totals.py
+++ b/tests/billing/test_totals.py
@@ -22,3 +22,9 @@ def test_total_with_tax():
     assert invoice_total(lines, Decimal("0.20")) == Decimal("24.00")
+
+
+def test_line_totals_round_before_summing():
+    lines = [Line(qty=3, unit_price=Decimal("0.335")), Line(qty=3, unit_price=Decimal("0.335"))]
+    # each line is 1.005 -> 1.01, so the subtotal is 2.02, not 2.01
+    assert invoice_total(lines, Decimal("0")) == Decimal("2.02")