diff --git a/README.md b/README.md
index ea4a6f5..98aa12d 100644
--- a/README.md
+++ b/README.md
@@ -6,8 +6,7 @@
 [![Build status](https://github.com/cbonnell/pyasn1-fasder/actions/workflows/CI.yml/badge.svg)](https://github.com/cbonnell/pyasn1-fasder/actions/workflows/CI.yml)
 [![GitHub license](https://img.shields.io/pypi/l/pyasn1-fasder)](https://raw.githubusercontent.com/cbonnell/pyasn1-fasder/main/LICENSE)
 
-pyasn1-fasder is a DER decoder for pyasn1 with a focus on performance (relative to the decoder included with pyasn1) and
-checking the correctness of encoding. This decoder is more pedantic than most other decoders in terms of flagging DER
+pyasn1-fasder is a DER decoder for pyasn1 with a focus on checking the correctness of encoding. This decoder is more pedantic than most other decoders in terms of flagging DER
 encoding errors, and this behavior is  unlikely to change.
 
 ## Installation
diff --git a/tests/test_basic.py b/tests/test_basic.py
index 898c3ad..219c820 100644
--- a/tests/test_basic.py
+++ b/tests/test_basic.py
@@ -24,3 +24,10 @@ def test_base_case():
     assert rest == b''
 
     assert decoded.hasValue() and bytes(decoded) == b'\x61\x62\x63'
+
+
+def test_trailing_octets():
+    octet_string = b'\x04\x01\x61\x62\x63'
+
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = decode_der(octet_string, asn1Spec=univ.OctetString())
diff --git a/tests/test_universal_primitive.py b/tests/test_universal_primitive.py
new file mode 100644
index 0000000..76107b6
--- /dev/null
+++ b/tests/test_universal_primitive.py
@@ -0,0 +1,124 @@
+import binascii
+
+import pytest
+from pyasn1.error import PyAsn1Error
+
+from pyasn1.type import univ, char, namedval
+
+from pyasn1_fasder import decode_der
+
+
+def _wrapper(substrate_hex, asn1Spec):
+    return decode_der(binascii.unhexlify(substrate_hex), asn1Spec=asn1Spec)
+
+
+def test_boolean_true():
+    decoded, _ = _wrapper(b'0101FF', univ.Boolean())
+    assert bool(decoded)
+
+
+def test_boolean_false():
+    decoded, _ = _wrapper(b'010100', univ.Boolean())
+    assert not bool(decoded)
+
+
+def test_boolean_bad_length():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'01020000', univ.Boolean())
+
+
+def test_boolean_bad_true_value():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'010101', univ.Boolean())
+
+
+def test_integer_positive():
+    decoded, _ = _wrapper(b'020101', univ.Integer())
+
+    assert int(decoded) == 1
+
+
+def test_integer_negative():
+    decoded, _ = _wrapper(b'0201FF', univ.Integer())
+
+    assert int(decoded) == -1
+
+
+def test_integer_zero_extra_octet():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'02020000', univ.Integer())
+
+
+def test_integer_one_leading_zero():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'0202007F', univ.Integer())
+
+
+def test_integer_negative_one_leading_all_one_bits():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'0202FFFF', univ.Integer())
+
+
+def test_bitstring_no_trailer_bit_count():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'0300', univ.BitString())
+
+
+def test_bitstring_nonzero_trailer_bit_count_no_value_octets():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'030101', univ.BitString())
+
+
+def test_bitstring_trailer_bit_count_overflow():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'03020800', univ.BitString())
+
+
+def test_bitstring_one_value_no_trailer():
+    decoded, _ = _wrapper(b'03020001', univ.BitString())
+
+    assert decoded.asOctets() == b'\x01'
+
+
+def test_bitstring_one_value_with_trailer():
+    decoded, _ = _wrapper(b'03020102', univ.BitString())
+
+    assert decoded.asOctets() == b'\x01'
+
+
+class NamedBitString(univ.BitString):
+    pass
+
+
+NamedBitString.namedValues = namedval.NamedValues(
+    ('foo', 0),
+    ('bar', 1),
+    ('baz', 2),
+)
+
+
+def test_named_bitstring_non_minimal_encoding():
+    with pytest.raises(PyAsn1Error):
+        _wrapper(b'03020002', NamedBitString())
+
+
+def test_null():
+    decoded, _ = _wrapper(b'0500', univ.Null())
+
+    assert str(decoded) == ''
+
+
+def test_null_too_long():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'0501FF', univ.Null())
+
+
+def test_printablestring():
+    decoded, _ = _wrapper(b'1303414243', char.PrintableString())
+
+    assert str(decoded) == 'ABC'
+
+
+def test_printablestring_badchar():
+    with pytest.raises(PyAsn1Error):
+        decoded, _ = _wrapper(b'13017E', char.PrintableString())