diff --git a/lib/secretariat/invoice.rb b/lib/secretariat/invoice.rb
index 140627b..0fac5d3 100644
--- a/lib/secretariat/invoice.rb
+++ b/lib/secretariat/invoice.rb
@@ -95,11 +95,11 @@ def taxes
       line_items.each do |line_item|
         if line_item.tax_percent.nil?
           taxes['0'] = Tax.new(tax_percent: BigDecimal(0), tax_category: line_item.tax_category, tax_amount: BigDecimal(0)) if taxes['0'].nil?
-          taxes['0'].base_amount += BigDecimal(line_item.net_amount) * line_item.billed_quantity
+          taxes['0'].base_amount += line_item.signed_charge_amount
         else
           taxes[line_item.tax_percent] = Tax.new(tax_percent: BigDecimal(line_item.tax_percent), tax_category: line_item.tax_category) if taxes[line_item.tax_percent].nil?
           taxes[line_item.tax_percent].tax_amount += BigDecimal(line_item.tax_amount)
-          taxes[line_item.tax_percent].base_amount += BigDecimal(line_item.net_amount) * line_item.billed_quantity
+          taxes[line_item.tax_percent].base_amount += line_item.signed_charge_amount
         end
       end
 
@@ -132,9 +132,10 @@ def valid?
         return false
       end
       if tax_calculation_method == :ITEM_BASED
-        line_items_tax_amount = line_items.sum(&:tax_amount)
-        if tax_amount != line_items_tax_amount
-          @errors << "Tax amount #{tax_amount} and summed up item tax amounts #{line_items_tax_amount} deviate"
+        line_items_tax_amount = line_items.sum(BigDecimal(0)) { |item| BigDecimal(item.tax_amount) }
+        if tax != line_items_tax_amount
+          @errors << "Tax amount #{tax.to_s('F')} and summed up item tax amounts #{line_items_tax_amount.to_s('F')} deviate"
+          return false
         end
       elsif tax_calculation_method != :NONE
         taxes.each do |tax|
diff --git a/lib/secretariat/line_item.rb b/lib/secretariat/line_item.rb
index 8f7a683..27f5c28 100644
--- a/lib/secretariat/line_item.rb
+++ b/lib/secretariat/line_item.rb
@@ -18,6 +18,12 @@
 module Secretariat
 
 
+  # A line's VAT may differ from net x rate by rounding: when the gross price is
+  # fixed and net and VAT are derived from it, the VAT can be a cent off the
+  # recalculated value. EN 16931 has no line VAT amount, so this only bounds the
+  # amounts the line contributes to the VAT breakdown.
+  LINE_TAX_ROUNDING_TOLERANCE = BigDecimal('0.01')
+
   LineItem = Struct.new('LineItem',
     :name,
     :billed_quantity,
@@ -93,7 +99,7 @@ def valid?
         calculated_tax = charge_price * BigDecimal(tax_percent) / BigDecimal(100)
         calculated_tax = calculated_tax.round(2)
         calculated_tax = -calculated_tax if billed_quantity.negative?
-        if calculated_tax != tax
+        if (calculated_tax - tax).abs > LINE_TAX_ROUNDING_TOLERANCE
           @errors << "Tax and calculated tax deviate: #{tax} / #{calculated_tax}"
           return false
         end
@@ -101,6 +107,13 @@ def valid?
       return true
     end
 
+    # The line total (BT-131) as it adds up to the VAT base: negative for a
+    # negative quantity, since the amounts themselves are kept positive.
+    def signed_charge_amount
+      charge = BigDecimal(charge_amount)
+      billed_quantity.negative? ? -charge : charge
+    end
+
     def unit_code
       UNIT_CODES[unit] || 'C62'
     end
diff --git a/test/invoice_test.rb b/test/invoice_test.rb
index 8af2c76..eb6be47 100644
--- a/test/invoice_test.rb
+++ b/test/invoice_test.rb
@@ -861,6 +861,106 @@ def test_fr_invoice
       assert_match(%r{<ram:SpecifiedLegalOrganization>\s*<ram:ID schemeID="0002">304755032</ram:ID>\s*</ram:SpecifiedLegalOrganization>}, xml)
     end
 
+    # A gross-leading row: the gross price is fixed, net and VAT are derived from
+    # it, so the row's VAT (27.21) is one cent below net x rate (27.2153 -> 27.22).
+    def make_gross_leading_invoice(line_tax:, invoice_tax:)
+      line_item = LineItem.new(
+        name: '8 x Overnight stay',
+        billed_quantity: BigDecimal('8'),
+        unit: :PIECE,
+        gross_amount: BigDecimal('52'),
+        net_amount: BigDecimal('48.59875'),
+        charge_amount: BigDecimal('388.79'),
+        tax_category: :STANDARDRATE,
+        tax_percent: '7',
+        tax_amount: line_tax,
+        origin_country_code: 'DE',
+        currency_code: 'EUR'
+      )
+      invoice = make_de_invoice
+      invoice.currency_code = 'EUR'
+      invoice.tax_calculation_method = :ITEM_BASED
+      invoice.line_items = [line_item]
+      invoice.basis_amount = '388.79'
+      invoice.tax_amount = invoice_tax
+      invoice.grand_total_amount = (BigDecimal('388.79') + BigDecimal(invoice_tax)).to_s('F')
+      invoice.due_amount = invoice.grand_total_amount
+      invoice.paid_amount = 0
+      invoice
+    end
+
+    def test_item_based_invoice_keeps_line_vat_rounded_from_the_gross_price
+      invoice = make_gross_leading_invoice(line_tax: BigDecimal('27.21'), invoice_tax: '27.21')
+
+      assert invoice.valid?, invoice.errors.inspect
+      xml = invoice.to_xml(version: 2)
+      assert_match(%r{<ram:CalculatedAmount>27.21</ram:CalculatedAmount>}, xml)
+      assert_match(%r{<ram:GrandTotalAmount>416.00</ram:GrandTotalAmount>}, xml)
+    end
+
+    def test_line_vat_more_than_a_cent_off_is_still_rejected
+      line_item = make_gross_leading_invoice(line_tax: BigDecimal('27.20'), invoice_tax: '27.20').line_items.first
+
+      refute line_item.valid?
+      assert_equal ["Tax and calculated tax deviate: 0.272e2 / 0.2722e2"], line_item.errors
+    end
+
+    def test_item_based_totals_passed_as_strings_leave_no_errors
+      invoice = make_gross_leading_invoice(line_tax: BigDecimal('27.21'), invoice_tax: '27.21')
+
+      assert invoice.valid?
+      assert_equal [], invoice.errors
+    end
+
+    def test_item_based_invoice_rejects_a_tax_total_that_differs_from_its_lines
+      invoice = make_de_invoice
+      invoice.tax_calculation_method = :ITEM_BASED
+      untaxed = invoice.line_items.first
+      untaxed.tax_category = :UNTAXEDSERVICE
+      untaxed.tax_percent = nil
+      untaxed.tax_amount = BigDecimal('3.80')
+      invoice.tax_amount = BigDecimal('0')
+      invoice.grand_total_amount = BigDecimal('20')
+
+      refute invoice.valid?
+      assert_equal ["Tax amount 0.0 and summed up item tax amounts 3.8 deviate"], invoice.errors
+    end
+
+    # Two days, 120 participants, 5,000.00 net per day: the unit price is stored
+    # with four decimals (41.6667), so 41.6667 x 120 = 5000.004 while each line
+    # total is 5000.00. Summing unit price x quantity drifts to 10000.008 and
+    # rounds to 10000.01, a cent off the lines it is made of.
+    def test_vat_base_is_the_sum_of_the_line_totals
+      line_items = %w[Day1 Day2].map do |day|
+        LineItem.new(
+          name: "Conference package #{day}",
+          billed_quantity: BigDecimal('120'),
+          unit: :PIECE,
+          gross_amount: BigDecimal('41.6667'),
+          net_amount: BigDecimal('41.6667'),
+          charge_amount: BigDecimal('5000.00'),
+          tax_category: :STANDARDRATE,
+          tax_percent: '19',
+          tax_amount: BigDecimal('950.00'),
+          origin_country_code: 'DE',
+          currency_code: 'EUR'
+        )
+      end
+      invoice = make_de_invoice
+      invoice.currency_code = 'EUR'
+      invoice.tax_calculation_method = :ITEM_BASED
+      invoice.line_items = line_items
+      invoice.basis_amount = '10000.00'
+      invoice.tax_amount = '1900.00'
+      invoice.grand_total_amount = '11900.00'
+      invoice.due_amount = '11900.00'
+      invoice.paid_amount = 0
+
+      assert invoice.valid?, invoice.errors.inspect
+      xml = invoice.to_xml(version: 2)
+      assert_match(%r{<ram:BasisAmount>10000.00</ram:BasisAmount>}, xml)
+    end
+
     def test_invoice_with_quantity_causing_sub_cent_amounts
       errors = []