diff --git a/tests/generators/ssz_generic/ssz_container.py b/tests/generators/ssz_generic/ssz_container.py
index 8f3a59ce3..9c1d9d0cb 100644
--- a/tests/generators/ssz_generic/ssz_container.py
+++ b/tests/generators/ssz_generic/ssz_container.py
@@ -105,7 +105,7 @@ def invalid_cases():
                          RandomizationMode.mode_one_count,
                          RandomizationMode.mode_max_count]:
                 if len(offsets) != 0:
-                    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)),
@@ -118,3 +118,20 @@ def invalid_cases():
                                   offset_index=offset_index,
                                   change=lambda x: 0
                               ))
+                        if index == 0:
+                            yield f'{name}_{mode.to_name()}_first 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[0:2]
+                            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[0:1]
+                            yield f'{name}_{mode.to_name()}_last offset_{offset_index}_wrong_byte_length', \
+                                invalid_test_case(lambda:serialized)