diff --git a/tests/test_decode_event.py b/tests/test_decode_event.py
index 3e55c42..11635b6 100644
--- a/tests/test_decode_event.py
+++ b/tests/test_decode_event.py
@@ -2,7 +2,7 @@
 
 import pytest
 
-from eth_event import EventError, decode_event, decode_logs
+from eth_event import EventError, UnknownEvent, decode_event, decode_logs
 
 
 def test_decode_event(log, abi):
@@ -25,12 +25,32 @@ def test_decode_logs(log, complex_log, abi):
     decode_logs([log, complex_log], abi)
 
 
-def test_decode_logs_anonymous(anon_a_log, anon_b_log, complex_log, abi):
+def test_decode_logs_allow_undecoded(anon_a_log, anon_b_log, complex_log, abi):
     logs = [anon_a_log, complex_log, anon_b_log]
-    with pytest.raises(EventError):
-        decode_logs(logs, abi, skip_anonymous=False)
-    events = decode_logs(logs, abi)
-    assert len(events) == 1
+    events = decode_logs(logs, abi, allow_undecoded=True)
+
+    assert len(events) == 3
+    assert len([i for i in events if i["decoded"]]) == 1
+
+
+def test_decode_logs_not_allow_undecoded(anon_a_log, abi):
+    logs = [anon_a_log]
+    with pytest.raises(UnknownEvent):
+        decode_logs(logs, abi, allow_undecoded=False)
+
+
+def test_decode_logs_no_topic(anon_a_log, abi):
+    logs = [anon_a_log]
+    event = decode_logs(logs, abi, allow_undecoded=True)
+
+    assert event == [
+        {
+            "name": None,
+            "data": "0x00000000000000000000000066ab6d9362d4f35596279692f0251db635165871",
+            "topics": [],
+            "decoded": False,
+        }
+    ]
 
 
 def test_decode_insufficient(complex_log, abi):
diff --git a/tests/test_decode_trace.py b/tests/test_decode_trace.py
index 5bea787..b009711 100644
--- a/tests/test_decode_trace.py
+++ b/tests/test_decode_trace.py
@@ -5,7 +5,7 @@
 
 import pytest
 
-from eth_event import StructLogError, decode_trace
+from eth_event import StructLogError, UnknownEvent, decode_trace
 
 
 # LOG events are at indexes 378 and 536
@@ -46,3 +46,12 @@ def test_decode_raises(abi, raw_trace):
     del trace[378]["stack"]
     with pytest.raises(StructLogError):
         decode_trace(raw_trace["result"]["structLogs"][:400], abi)
+
+
+def test_allow_undecoded(raw_trace):
+    decode_trace(raw_trace, [], allow_undecoded=True)
+
+
+def test_not_allow_undecoded(raw_trace):
+    with pytest.raises(UnknownEvent):
+        decode_trace(raw_trace, [], allow_undecoded=False)