diff --git a/tests/app/letters/test_letter_utils.py b/tests/app/letters/test_letter_utils.py
index 758c35021..efa55bc0b 100644
--- a/tests/app/letters/test_letter_utils.py
+++ b/tests/app/letters/test_letter_utils.py
@@ -27,3 +27,13 @@ def test_is_precompiled_letter_true(sample_letter_template):
     sample_letter_template.hidden = True
     sample_letter_template.name = current_app.config['PRECOMPILED_TEMPLATE_NAME']
     assert is_precompiled_letter(sample_letter_template)
+
+
+def test_is_precompiled_letter_hidden_true_not_name(sample_letter_template):
+    sample_letter_template.hidden = True
+    assert not is_precompiled_letter(sample_letter_template)
+
+
+def test_is_precompiled_letter_name_correct_not_hidden(sample_letter_template):
+    sample_letter_template.name = current_app.config['PRECOMPILED_TEMPLATE_NAME']
+    assert not is_precompiled_letter(sample_letter_template)