diff --git a/multibase/converters.py b/multibase/converters.py
index 4202658..f4f0347 100644
--- a/multibase/converters.py
+++ b/multibase/converters.py
@@ -7,8 +7,17 @@
 
 class BaseStringConverter(BaseConverter):
     def encode(self, bytes):
+        bytes = ensure_bytes(bytes)
+        if len(bytes) == 0:
+            return b""
+
+        leading_zeros = len(bytes) - len(bytes.lstrip(b"\x00"))
+        if leading_zeros == len(bytes):
+            return str(self.digits[0] * leading_zeros).encode("utf-8")
+
         number = int.from_bytes(bytes, byteorder="big", signed=False)
-        return ensure_bytes(super().encode(number))
+        encoded = super().encode(number)
+        return ensure_bytes(self.digits[0] * leading_zeros + encoded)
 
     def bytes_to_int(self, bytes):
         length = len(bytes)
@@ -19,12 +28,20 @@ def bytes_to_int(self, bytes):
             value += self.digits.index(chr(x)) * base ** (length - (i + 1))
         return value
 
-    def decode(self, bytes):
-        decoded_int = self.bytes_to_int(bytes)
+    def decode(self, data):
+        bytes_str = data.decode("utf-8") if isinstance(data, bytes) else data
+        if len(bytes_str) == 0:
+            return b""
+
+        leading_zeros = len(bytes_str) - len(bytes_str.lstrip(self.digits[0]))
+        if leading_zeros == len(bytes_str):
+            return b"\x00" * leading_zeros
+
+        decoded_int = self.bytes_to_int(data)
         # See https://docs.python.org/3.5/library/stdtypes.html#int.to_bytes for more about the magical expression
         # below
         decoded_data = decoded_int.to_bytes((decoded_int.bit_length() + 7) // 8, byteorder="big")
-        return decoded_data
+        return b"\x00" * leading_zeros + decoded_data
 
 
 class Base16StringConverter(BaseStringConverter):
@@ -44,12 +61,7 @@ def decode(self, data):
             data_str = data.decode("utf-8")
         else:
             data_str = data
-        # Convert to match our digits case
-        if self.uppercase:
-            data_str = data_str.upper()
-        else:
-            data_str = data_str.lower()
-        return super().decode(data_str.encode("utf-8"))
+        return bytes.fromhex(data_str)
 
 
 class BaseByteStringConverter:
diff --git a/tests/test_roundtrip.py b/tests/test_roundtrip.py
new file mode 100644
index 0000000..4d2ddf5
--- /dev/null
+++ b/tests/test_roundtrip.py
@@ -0,0 +1,45 @@
+import os
+
+import pytest
+
+from multibase import ENCODINGS, decode, encode
+
+
+@pytest.mark.parametrize("encoding_info", ENCODINGS, ids=lambda e: e.encoding)
+def test_random_data(encoding_info):
+    """Round-trip random data of various sizes."""
+    for size in [1, 2, 7, 16, 32, 64, 137, 256, 1024]:
+        data = os.urandom(size)
+        encoded = encode(encoding_info.encoding, data)
+        decoded = decode(encoded)
+        assert decoded == data, f"Failed for {encoding_info.encoding} size={size}"
+
+
+@pytest.mark.parametrize("encoding_info", ENCODINGS, ids=lambda e: e.encoding)
+def test_leading_zeros(encoding_info):
+    """Round-trip data with leading zero bytes."""
+    for num_zeros in [1, 2, 4, 8, 16]:
+        data = b"\x00" * num_zeros + b"hello"
+        encoded = encode(encoding_info.encoding, data)
+        decoded = decode(encoded)
+        assert decoded == data, f"Leading zeros lost for {encoding_info.encoding} zeros={num_zeros}"
+
+
+@pytest.mark.parametrize("encoding_info", ENCODINGS, ids=lambda e: e.encoding)
+def test_all_zeros(encoding_info):
+    """Round-trip all-zero data."""
+    for size in [1, 4, 16, 32]:
+        data = b"\x00" * size
+        encoded = encode(encoding_info.encoding, data)
+        decoded = decode(encoded)
+        assert decoded == data
+
+
+@pytest.mark.parametrize("encoding_info", ENCODINGS, ids=lambda e: e.encoding)
+def test_all_ones(encoding_info):
+    """Round-trip all-0xFF data."""
+    for size in [1, 4, 16, 32]:
+        data = b"\xff" * size
+        encoded = encode(encoding_info.encoding, data)
+        decoded = decode(encoded)
+        assert decoded == data