diff --git a/asyncpg/protocol/codecs/tid.pyx b/asyncpg/protocol/codecs/tid.pyx
index 85f0aed5..fef7e7c3 100644
--- a/asyncpg/protocol/codecs/tid.pyx
+++ b/asyncpg/protocol/codecs/tid.pyx
@@ -7,7 +7,7 @@
 
 cdef tid_encode(ConnectionSettings settings, WriteBuffer buf, obj):
     cdef int overflow = 0
-    cdef long block, offset
+    cdef unsigned long block, offset
 
     if not (cpython.PyTuple_Check(obj) or cpython.PyList_Check(obj)):
         raise TypeError(
@@ -18,25 +18,24 @@ cdef tid_encode(ConnectionSettings settings, WriteBuffer buf, obj):
             'invalid number of elements in tid tuple, expecting 2')
 
     try:
-        block = cpython.PyLong_AsLong(obj[0])
+        block = cpython.PyLong_AsUnsignedLong(obj[0])
     except OverflowError:
         overflow = 1
 
     # "long" and "long long" have the same size for x86_64, need an extra check
-    if overflow or (sizeof(block) > 4 and (block < -2147483648 or
-                                                 block > 2147483647)):
+    if overflow or (sizeof(block) > 4 and block > 4294967295):
         raise OverflowError(
-            'block too big to be encoded as INT4: {!r}'.format(obj[0]))
+            'block too big to be encoded as UINT4: {!r}'.format(obj[0]))
 
     try:
-        offset = cpython.PyLong_AsLong(obj[1])
+        offset = cpython.PyLong_AsUnsignedLong(obj[1])
         overflow = 0
     except OverflowError:
         overflow = 1
 
-    if overflow or offset < -32768 or offset > 32767:
+    if overflow or offset > 65535:
         raise OverflowError(
-            'offset too big to be encoded as INT2: {!r}'.format(obj[1]))
+            'offset too big to be encoded as UINT2: {!r}'.format(obj[1]))
 
     buf.write_int32(6)
     buf.write_int32(<int32_t>block)
@@ -45,11 +44,11 @@ cdef tid_encode(ConnectionSettings settings, WriteBuffer buf, obj):
 
 cdef tid_decode(ConnectionSettings settings, FastReadBuffer buf):
     cdef:
-        int32_t block
-        int16_t offset
+        uint32_t block
+        uint16_t offset
 
-    block = hton.unpack_int32(buf.read(4))
-    offset = hton.unpack_int16(buf.read(2))
+    block = <uint32_t>hton.unpack_int32(buf.read(4))
+    offset = <uint16_t>hton.unpack_int16(buf.read(2))
 
     return (block, offset)
 
diff --git a/tests/test_codecs.py b/tests/test_codecs.py
index 5ed7d2b6..cf93be69 100644
--- a/tests/test_codecs.py
+++ b/tests/test_codecs.py
@@ -380,7 +380,13 @@ def _timezone(offset):
         asyncpg.Circle((0.0, 0.0), 100),
     ]),
     ('tid', 'tid', [
-        (0, 2),
+        (100, 200),
+        (0, 0),
+        (2147483647, 0),
+        (4294967295, 0),
+        (0, 32767),
+        (0, 65535),
+        (4294967295, 65535),
     ]),
 ]
 
@@ -611,20 +617,18 @@ async def test_invalid_input(self):
                 [1, 2, 3],
                 (4,),
             ]),
-            ('tid', OverflowError, 'block too big to be encoded as INT4', [
+            ('tid', OverflowError, 'block too big to be encoded as UINT4', [
+                (-1, 0),
                 (2**256, 0),
-                (decimal.Decimal("2000000000000000000000000000000"), 0),
-                (0xffffffff, 0),
-                (2**31, 0),
-                (-2**31 - 1, 0),
+                (0xffffffff + 1, 0),
+                (2**32, 0),
             ]),
-            ('tid', OverflowError, 'offset too big to be encoded as INT2', [
+            ('tid', OverflowError, 'offset too big to be encoded as UINT2', [
+                (0, -1),
                 (0, 2**256),
-                (0, decimal.Decimal("2000000000000000000000000000000")),
-                (0, 0xffff),
+                (0, 0xffff + 1),
                 (0, 0xffffffff),
-                (0, 32768),
-                (0, -32769),
+                (0, 65536),
             ]),
         ]