diff --git a/lib/fbe/award.rb b/lib/fbe/award.rb
index ae6eeb43..f1fc3d9c 100644
--- a/lib/fbe/award.rb
+++ b/lib/fbe/award.rb
@@ -379,6 +379,8 @@ def line(value, text)
     # Calculates the total points in this bill.
     #
     # @return [Integer] The sum of all point values, rounded to an integer
+    # @note The sum is rounded once, at the end, not line by line, so that
+    #   a clause worth half a point costs half a point and not a whole one
     # @example
     #   bill = Fbe::Award::Bill.new
     #   bill.line(42.5, "for answer")
@@ -396,7 +398,11 @@ def points
     #   bill.line(25, "for documentation")
     #   bill.greeting #=> "You've earned +75 points for this: +50 for code review; +25 for documentation. "
     def greeting
-      items = @lines.map { |l| "#{format('%+d', whole(l[:v]))} #{l[:t]}" }
+      items =
+        @lines.zip(portions).filter_map do |l, v|
+          next if v.zero?
+          "#{format('%+d', v)} #{l[:t]}"
+        end
       case items.size
       when 0
         "You've earned nothing. "
@@ -416,6 +422,24 @@ def greeting
     def whole(value)
       Integer(Float(value).round)
     end
+
+    # Splits the total between the lines, giving each one a whole number.
+    #
+    # Every line is rounded on its own first, and then the difference
+    # between what that adds up to and the total, which is rounded once,
+    # is handed to the lines with the largest remainders. So the numbers
+    # in the greeting still add up to the number in front of it.
+    #
+    # @return [Array<Integer>] One whole number per line, summing to +points+
+    def portions
+      ints = @lines.map { |l| whole(l[:v]) }
+      diff = points - ints.sum
+      return ints if diff.zero?
+      step = diff.negative? ? -1 : 1
+      order = (0...ints.size).sort_by { |i| (ints[i] - @lines[i][:v]) * step }
+      diff.abs.times { |k| ints[order[k % ints.size]] += step }
+      ints
+    end
   end
 
   # A class for generating human-readable bylaws.
diff --git a/test/fbe/test_award.rb b/test/fbe/test_award.rb
index b13c5c3d..41c732fb 100644
--- a/test/fbe/test_award.rb
+++ b/test/fbe/test_award.rb
@@ -174,6 +174,24 @@ def test_rounds_the_sum_once
     assert_equal(1, bill.points)
   end
 
+  def test_rounds_the_total_and_not_every_line
+    b = Fbe::Award.new('(award (give 8 "as a basis") (give -0.5 "for one day of delay"))').bill
+    assert_equal(8, b.points, b.greeting)
+    b = Fbe::Award.new('(award (give 8 "as a basis") (give -1.5 "for three days of delay"))').bill
+    assert_equal(7, b.points, b.greeting)
+  end
+
+  def test_lines_add_up_to_the_total_with_halves
+    b = Fbe::Award.new('(award (give 8 "as a basis") (give -1.5 "for delay"))').bill
+    g = b.greeting
+    assert_equal("You've earned +7 points for this: +8 as a basis; -1 for delay. ", g)
+  end
+
+  def test_skips_a_line_that_is_worth_nothing
+    g = Fbe::Award.new('(award (give 8 "as a basis") (give -0.4 "for delay"))').bill.greeting
+    assert_equal("You've earned +8 points. ", g)
+  end
+
   def test_shorten_when_one_number
     g = Fbe::Award.new('(award (give 23 "for love"))').bill.greeting
     assert_equal('You\'ve earned +23 points. ', g, g)