diff --git a/base62.py b/base62.py
index cc96a6f..e02ba13 100644
--- a/base62.py
+++ b/base62.py
@@ -16,24 +16,18 @@
 CHARSET_INVERTED = "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
 
 
-def encode(n, minlen=1, charset=CHARSET_DEFAULT):
+def encode(n, charset=CHARSET_DEFAULT):
     """Encodes a given integer ``n``."""
 
     chs = []
     while n > 0:
-        r = n % BASE
-        n //= BASE
+        n, r = divmod(n, BASE)
+        chs.insert(0, charset[r])
 
-        chs.append(charset[r])
+    if not chs:
+        return "0"
 
-    if len(chs) > 0:
-        chs.reverse()
-    else:
-        chs.append("0")
-
-    s = "".join(chs)
-    s = charset[0] * max(minlen - len(s), 0) + s
-    return s
+    return "".join(chs)
 
 
 def encodebytes(barray, charset=CHARSET_DEFAULT):
@@ -45,7 +39,27 @@ def encodebytes(barray, charset=CHARSET_DEFAULT):
     """
 
     _check_type(barray, bytes)
-    return encode(int.from_bytes(barray, "big"), charset=charset)
+
+    # Count the number of leading zeros.
+    leading_zeros_count = 0
+    for i in range(len(barray)):
+        if barray[i] != 0:
+            break
+        leading_zeros_count += 1
+
+    # Encode the leading zeros as "0" followed by a character indicating the count.
+    # This pattern may occur several times if there are many leading zeros.
+    n, r = divmod(leading_zeros_count, len(charset) - 1)
+    zero_padding = f"0{charset[-1]}" * n
+    if r:
+        zero_padding += f"0{charset[r]}"
+
+    # Special case: the input is empty, or is entirely null bytes.
+    if leading_zeros_count == len(barray):
+        return zero_padding
+
+    value = encode(int.from_bytes(barray, "big"), charset=charset)
+    return zero_padding + value
 
 
 def decode(encoded, charset=CHARSET_DEFAULT):
@@ -56,9 +70,6 @@ def decode(encoded, charset=CHARSET_DEFAULT):
     """
     _check_type(encoded, str)
 
-    if encoded.startswith("0z"):
-        encoded = encoded[2:]
-
     l, i, v = len(encoded), 0, 0
     for x in encoded:
         v += _value(x, charset=charset) * (BASE ** (l - (i + 1)))
@@ -75,6 +86,11 @@ def decodebytes(encoded, charset=CHARSET_DEFAULT):
     :rtype: bytes
     """
 
+    leading_null_bytes = b""
+    while encoded.startswith("0") and len(encoded) >= 2:
+        leading_null_bytes += b"\x00" * _value(encoded[1], charset)
+        encoded = encoded[2:]
+
     decoded = decode(encoded, charset=charset)
     buf = bytearray()
     while decoded > 0:
@@ -82,7 +98,7 @@ def decodebytes(encoded, charset=CHARSET_DEFAULT):
         decoded //= 256
     buf.reverse()
 
-    return bytes(buf)
+    return leading_null_bytes + bytes(buf)
 
 
 def _value(ch, charset):
diff --git a/tests/test_basic.py b/tests/test_basic.py
index 73f1d09..bade00f 100644
--- a/tests/test_basic.py
+++ b/tests/test_basic.py
@@ -4,7 +4,6 @@
 
 
 bytes_int_pairs = [
-    (b"\x00", 0),
     (b"\x01", 1),
     (b"\x01\x01", 0x0101),
     (b"\xff\xff", 0xFFFF),
@@ -20,9 +19,6 @@ def test_const():
 
 def test_basic():
     assert base62.encode(0) == "0"
-    assert base62.encode(0, minlen=0) == "0"
-    assert base62.encode(0, minlen=1) == "0"
-    assert base62.encode(0, minlen=5) == "00000"
     assert base62.decode("0") == 0
     assert base62.decode("0000") == 0
     assert base62.decode("000001") == 1
@@ -30,19 +26,11 @@ def test_basic():
     assert base62.encode(34441886726) == "base62"
     assert base62.decode("base62") == 34441886726
 
-    # NOTE: For backward compatibility. When I first wrote this module in PHP,
-    # I used to use the `0z` prefix to denote a base62 encoded string (similar
-    # to `0x` for hexadecimal strings).
-    assert base62.decode("0zbase62") == 34441886726
-
 
 def test_basic_inverted():
     kwargs = {"charset": base62.CHARSET_INVERTED}
 
     assert base62.encode(0, **kwargs) == "0"
-    assert base62.encode(0, minlen=0, **kwargs) == "0"
-    assert base62.encode(0, minlen=1, **kwargs) == "0"
-    assert base62.encode(0, minlen=5, **kwargs) == "00000"
     assert base62.decode("0", **kwargs) == 0
     assert base62.decode("0000", **kwargs) == 0
     assert base62.decode("000001", **kwargs) == 1
@@ -50,11 +38,6 @@ def test_basic_inverted():
     assert base62.encode(10231951886, **kwargs) == "base62"
     assert base62.decode("base62", **kwargs) == 10231951886
 
-    # NOTE: For backward compatibility. When I first wrote this module in PHP,
-    # I used to use the `0z` prefix to denote a base62 encoded string (similar
-    # to `0x` for hexadecimal strings).
-    assert base62.decode("0zbase62", **kwargs) == 10231951886
-
 
 @pytest.mark.parametrize("b, i", bytes_int_pairs)
 def test_bytes_to_int(b, i):
@@ -77,7 +60,7 @@ def test_encodebytes_rtype():
     assert isinstance(encoded, str)
 
 
-@pytest.mark.parametrize("s", ["0", "1", "a", "z", "ykzvd7ga", "0z1234"])
+@pytest.mark.parametrize("s", ["0", "1", "a", "z", "ykzvd7ga"])
 def test_decodebytes(s):
     assert int.from_bytes(base62.decodebytes(s), "big") == base62.decode(s)
 
@@ -113,3 +96,23 @@ def test_invalid_alphabet():
 def test_invalid_string():
     with pytest.raises(TypeError):
         base62.encodebytes({})
+
+
+@pytest.mark.parametrize(
+    "input_bytes, expected_encoded_text",
+    (
+        (b"", ""),
+        (b"\x00", "01"),
+        (b"\x00\x00", "02"),
+        (b"\x00\x01", "011"),
+        (b"\x00" * 61, "0z"),
+        (b"\x00" * 62, "0z01"),
+    ),
+)
+def test_leading_zeros(input_bytes, expected_encoded_text):
+    """Verify that leading null bytes are not lost."""
+
+    encoded_text = base62.encodebytes(input_bytes)
+    assert encoded_text == expected_encoded_text
+    output_bytes = base62.decodebytes(encoded_text)
+    assert output_bytes == input_bytes