diff --git a/lib/util.py b/lib/util.py
index 1c70dbd..f94a1ed 100644
--- a/lib/util.py
+++ b/lib/util.py
@@ -160,7 +160,7 @@ def int_to_bytes(value):
 def int_to_varint(value):
     '''Converts an integer to a Bitcoin-like varint bytes'''
     if value < 0:
-        raise Exception("attempt to write size < 0")
+        raise ValueError("attempt to write size < 0")
     elif value < 253:
         return pack('<B', value)
     elif value < 2**16:
@@ -316,4 +316,4 @@ unpack_uint16_from = Struct('<H').unpack_from
 unpack_uint32_from = Struct('<I').unpack_from
 unpack_uint64_from = Struct('<Q').unpack_from
 
-hex_to_bytes = bytes.fromhex
\ No newline at end of file
+hex_to_bytes = bytes.fromhex
diff --git a/tests/lib/test_util.py b/tests/lib/test_util.py
index 74411b4..5a3e9e5 100644
--- a/tests/lib/test_util.py
+++ b/tests/lib/test_util.py
@@ -1,6 +1,55 @@
+import os
+
+import pytest
+
 from lib import util
 
 
+class LoggedClassTest(util.LoggedClass):
+
+    def __init__(self):
+        super().__init__()
+        self.logger.info = self.note_info
+        self.logger.warning = self.note_warning
+        self.logger.error = self.note_error
+
+    def note_info(self, msg):
+        self.info_msg = msg
+
+    def note_warning(self, msg):
+        self.warning_msg = msg
+
+    def note_error(self, msg):
+        self.error_msg = msg
+
+
+def test_LoggedClass():
+    test = LoggedClassTest()
+    assert test.log_prefix == ''
+    test.log_prefix = 'prefix'
+    test.log_error('an error')
+    assert test.error_msg == 'prefixan error'
+    test.log_warning('a warning')
+    assert test.warning_msg == 'prefixa warning'
+    test.log_info('some info')
+    assert test.info_msg == 'prefixsome info'
+
+    assert test.throttled == 0
+    test.log_info('some info', throttle=True)
+    assert test.throttled == 1
+    assert test.info_msg == 'prefixsome info'
+    test.log_info('some info', throttle=True)
+    assert test.throttled == 2
+    assert test.info_msg == 'prefixsome info'
+    test.log_info('some info', throttle=True)
+    assert test.throttled == 3
+    assert test.info_msg == 'prefixsome info (throttling later logs)'
+    test.info_msg = ''
+    test.log_info('some info', throttle=True)
+    assert test.throttled == 4
+    assert test.info_msg == ''
+
+
 def test_cachedproperty():
     class Target:
 
@@ -23,9 +72,19 @@ def test_cachedproperty():
     assert t.prop == t.prop == 1
     assert Target.cls_prop == Target.cls_prop == 1
 
+def test_formatted_time():
+    assert util.formatted_time(0) == '00s'
+    assert util.formatted_time(59) == '59s'
+    assert util.formatted_time(60) == '01m 00s'
+    assert util.formatted_time(3599) == '59m 59s'
+    assert util.formatted_time(3600) == '01h 00m 00s'
+    assert util.formatted_time(3600*24) == '1d 00h 00m'
+    assert util.formatted_time(3600*24*367) == '367d 00h 00m'
+    assert util.formatted_time(3600*24, ':') == '1d:00h:00m'
 
 def test_deep_getsizeof():
     int_t = util.deep_getsizeof(1)
+    assert util.deep_getsizeof('foo') == util.deep_getsizeof('') + 3
     assert util.deep_getsizeof([1, 1]) > 2 * int_t
     assert util.deep_getsizeof({1: 1}) > 2 * int_t
     assert util.deep_getsizeof({1: {1: 1}}) > 3 * int_t
@@ -57,6 +116,73 @@ def test_increment_byte_string():
     assert util.increment_byte_string(b'\x01\x01') == b'\x01\x02'
     assert util.increment_byte_string(b'\xff\xff') is None
 
+def test_bytes_to_int():
+    assert util.bytes_to_int(b'\x07[\xcd\x15') == 123456789
+
+def test_int_to_bytes():
+    assert util.int_to_bytes(456789) == b'\x06\xf8U'
+
+def test_int_to_varint():
+    with pytest.raises(ValueError):
+        util.int_to_varint(-1)
+    assert util.int_to_varint(0) == b'\0'
+    assert util.int_to_varint(5) == b'\5'
+    assert util.int_to_varint(252) == b'\xfc'
+    assert util.int_to_varint(253) == b'\xfd\xfd\0'
+    assert util.int_to_varint(65535) == b'\xfd\xff\xff'
+    assert util.int_to_varint(65536) == b'\xfe\0\0\1\0'
+    assert util.int_to_varint(2**32-1) == b'\xfe\xff\xff\xff\xff'
+    assert util.int_to_varint(2**32) == b'\xff\0\0\0\0\1\0\0\0'
+    assert util.int_to_varint(2**64-1) \
+        == b'\xff\xff\xff\xff\xff\xff\xff\xff\xff'
+
+def test_LogicalFile(tmpdir):
+    prefix = os.path.join(tmpdir, 'log')
+    L = util.LogicalFile(prefix, 2, 6)
+    with pytest.raises(FileNotFoundError):
+        L.open_file(0, create=False)
+
+    # Check L.open creates a file
+    with L.open_file(8, create=True) as f:
+        pass
+    with util.open_file(prefix + '01') as f:
+        pass
+
+    L.write(0, b'987')
+    assert L.read(0, -1) == b'987'
+    assert L.read(0, 4) == b'987'
+    assert L.read(1, 1) == b'8'
+
+    L.write(0, b'01234567890')
+    assert L.read(0, -1) == b'01234567890'
+    assert L.read(5, -1) == b'567890'
+    with util.open_file(prefix + '01') as f:
+        assert f.read(-1) == b'67890'
+
+    # Test file boundary
+    L.write(0, b'957' * 6)
+    assert L.read(0, -1) == b'957' * 6
+
+def test_open_fns(tmpdir):
+    tmpfile = os.path.join(tmpdir, 'file1')
+    with pytest.raises(FileNotFoundError):
+        util.open_file(tmpfile)
+    with util.open_file(tmpfile, create=True) as f:
+        f.write(b'56')
+    with util.open_file(tmpfile) as f:
+        assert f.read(3) == b'56'
+
+    # Test open_truncate truncates and creates
+    with util.open_truncate(tmpfile) as f:
+        assert f.read(3) == b''
+    tmpfile = os.path.join(tmpdir, 'file2')
+    with util.open_truncate(tmpfile) as f:
+        assert f.read(3) == b''
+
+def test_address_string():
+    assert util.address_string(('foo.bar', 84)) == 'foo.bar:84'
+    assert util.address_string(('1.2.3.4', 84)) == '1.2.3.4:84'
+    assert util.address_string(('0a::23', 84)) == '[a::23]:84'
 
 def test_is_valid_hostname():
     is_valid_hostname = util.is_valid_hostname
@@ -135,4 +261,4 @@ def test_unpackers():
 
 def test_hex_transforms():
     h = "AABBCCDDEEFF"
-    assert util.hex_to_bytes(h) == b'\xaa\xbb\xcc\xdd\xee\xff'
\ No newline at end of file
+    assert util.hex_to_bytes(h) == b'\xaa\xbb\xcc\xdd\xee\xff'