diff --git a/python/pmtiles/tile.py b/python/pmtiles/tile.py
index b8f6b00..692ef57 100644
--- a/python/pmtiles/tile.py
+++ b/python/pmtiles/tile.py
@@ -41,6 +41,10 @@ def t_on_level(z, pos):
 
 
 def zxy_to_tileid(z, x, y):
+    if z > 31:
+        raise OverflowError("tile zoom exceeds 64-bit limit")
+    if x > (1 << z) - 1 or y > (1 << z) - 1:
+        raise ValueError("tile x/y outside zoom level bounds")
     acc = 0
     tz = 0
     while tz < z:
@@ -70,13 +74,12 @@ def zxy_to_tileid(z, x, y):
 def tileid_to_zxy(tile_id):
     num_tiles = 0
     acc = 0
-    z = 0
-    while True:
+    for z in range(0,32):
         num_tiles = (1 << z) * (1 << z)
         if acc + num_tiles > tile_id:
             return t_on_level(z, tile_id - acc)
         acc += num_tiles
-        z += 1
+    raise OverflowError("tile zoom exceeds 64-bit limit")
 
 
 def find_tile(entries, tile_id):
diff --git a/python/test/test_tile.py b/python/test/test_tile.py
index 08e5f53..5f5de22 100644
--- a/python/test/test_tile.py
+++ b/python/test/test_tile.py
@@ -52,6 +52,27 @@ class TestTileId(unittest.TestCase):
                     self.assertEqual(x, rx)
                     self.assertEqual(y, ry)
 
+    def test_tile_extremes(self):
+        for z in range(0,32):
+            dim = (1 << z) - 1
+            tl = tileid_to_zxy(zxy_to_tileid(z,0,0))
+            self.assertEqual(tl,(z,0,0))
+            tr = tileid_to_zxy(zxy_to_tileid(z,dim,0))
+            self.assertEqual(tr,(z,dim,0))
+            bl = tileid_to_zxy(zxy_to_tileid(z,0,dim))
+            self.assertEqual(bl,(z,0,dim))
+            br = tileid_to_zxy(zxy_to_tileid(z,dim,dim))
+            self.assertEqual(br,(z,dim,dim))
+
+    def test_invalid_tiles(self):
+        with self.assertRaises(Exception) as context:
+            tileid_to_zxy(18446744073709551615)
+
+        with self.assertRaises(Exception) as context:
+            zxy_to_tileid(32,0,0)
+
+        with self.assertRaises(Exception) as context:
+            zxy_to_tileid(0,1,1)
 
 class TestFindTile(unittest.TestCase):
     def test_find_tile_missing(self):