diff --git a/tests/generators/ssz_generic/ssz_container.py b/tests/generators/ssz_generic/ssz_container.py
index 088a8ca54..1b30d687a 100644
--- a/tests/generators/ssz_generic/ssz_container.py
+++ b/tests/generators/ssz_generic/ssz_container.py
@@ -104,7 +104,7 @@ def invalid_cases():
                          RandomizationMode.mode_nil_count,
                          RandomizationMode.mode_one_count,
                          RandomizationMode.mode_max_count]:
-                for offset_index in offsets:
+                for index, offset_index in enumerate(offsets):
                     yield f'{name}_{mode.to_name()}_offset_{offset_index}_plus_one', \
                           invalid_test_case(lambda: mod_offset(
                               b=serialize(container_case_fn(rng, mode, typ)),
@@ -117,3 +117,20 @@ def invalid_cases():
                               offset_index=offset_index,
                               change=lambda x: 0
                           ))
+                    if index == 0:
+                        yield f'{name}_{mode.to_name()}_offset_{offset_index}_minus_one', \
+                            invalid_test_case(lambda: mod_offset(
+                              b=serialize(container_case_fn(rng, mode, typ)),
+                              offset_index=offset_index,
+                              change=lambda x: x - 1
+                            ))
+                    if mode == RandomizationMode.mode_max_count:
+                        serialized = serialize(container_case_fn(rng, mode, typ))
+                        serialized = serialized + serialized[:2]
+                        yield f'{name}_{mode.to_name()}_last_offset_{offset_index}_overflow', \
+                            invalid_test_case(lambda: serialized)
+                    if mode == RandomizationMode.mode_one_count:
+                        serialized = serialize(container_case_fn(rng, mode, typ))
+                        serialized = serialized + serialized[:1]
+                        yield f'{name}_{mode.to_name()}_last_offset_{offset_index}_wrong_byte_length', \
+                            invalid_test_case(lambda: serialized)