diff --git a/libp2p/exceptions.py b/libp2p/exceptions.py
index 0ea0078..ce2dc34 100644
--- a/libp2p/exceptions.py
+++ b/libp2p/exceptions.py
@@ -6,3 +6,7 @@ class ValidationError(BaseLibp2pError):
     """
     Raised when something does not pass a validation check.
     """
+
+
+class ParseError(BaseLibp2pError):
+    pass
diff --git a/libp2p/network/swarm.py b/libp2p/network/swarm.py
index 07b5e14..52df727 100644
--- a/libp2p/network/swarm.py
+++ b/libp2p/network/swarm.py
@@ -156,15 +156,10 @@ class Swarm(INetwork):
         if not addrs:
             raise SwarmException("No known addresses to peer")
 
-        multiaddr = addrs[0]
-
         muxed_conn = await self.dial_peer(peer_id)
 
-        # Use muxed conn to open stream, which returns
-        # a muxed stream
-        # TODO: Remove protocol id from being passed into muxed_conn
-        # FIXME: Remove multiaddr from being passed into muxed_conn
-        muxed_stream = await muxed_conn.open_stream(protocol_ids[0], multiaddr)
+        # Use muxed conn to open stream, which returns a muxed stream
+        muxed_stream = await muxed_conn.open_stream()
 
         # Perform protocol muxing to determine protocol to use
         selected_protocol = await self.multiselect_client.select_one_of(
diff --git a/libp2p/stream_muxer/abc.py b/libp2p/stream_muxer/abc.py
index 245a739..f16b805 100644
--- a/libp2p/stream_muxer/abc.py
+++ b/libp2p/stream_muxer/abc.py
@@ -1,8 +1,6 @@
 from abc import ABC, abstractmethod
 from typing import TYPE_CHECKING, Optional
 
-from multiaddr import Multiaddr
-
 from libp2p.peer.id import ID
 from libp2p.security.secure_conn_interface import ISecureConn
 from libp2p.stream_muxer.mplex.constants import HeaderTags
@@ -66,20 +64,15 @@ class IMuxedConn(ABC):
         Read a message from `stream_id`'s buffer, non-blockingly.
         """
 
-    # FIXME: Remove multiaddr from being passed into muxed_conn
     @abstractmethod
-    async def open_stream(
-        self, protocol_id: str, multi_addr: Multiaddr
-    ) -> "IMuxedStream":
+    async def open_stream(self) -> "IMuxedStream":
         """
         creates a new muxed_stream
-        :param protocol_id: protocol_id of stream
-        :param multi_addr: multi_addr that stream connects to
-        :return: a new stream
+        :return: a new ``IMuxedStream`` stream
         """
 
     @abstractmethod
-    async def accept_stream(self) -> None:
+    async def accept_stream(self, name: str) -> None:
         """
         accepts a muxed stream opened by the other end
         """
diff --git a/libp2p/stream_muxer/mplex/mplex.py b/libp2p/stream_muxer/mplex/mplex.py
index 8c78431..2dd2618 100644
--- a/libp2p/stream_muxer/mplex/mplex.py
+++ b/libp2p/stream_muxer/mplex/mplex.py
@@ -1,14 +1,16 @@
 import asyncio
 from typing import Dict, Optional, Tuple
 
-from multiaddr import Multiaddr
-
 from libp2p.network.typing import GenericProtocolHandlerFn
 from libp2p.peer.id import ID
 from libp2p.security.secure_conn_interface import ISecureConn
 from libp2p.stream_muxer.abc import IMuxedConn, IMuxedStream
 from libp2p.typing import TProtocol
-from libp2p.utils import decode_uvarint_from_stream, encode_uvarint
+from libp2p.utils import (
+    decode_uvarint_from_stream,
+    encode_uvarint,
+    read_varint_prefixed_bytes,
+)
 
 from .constants import HeaderTags
 from .exceptions import StreamNotFound
@@ -31,6 +33,7 @@ class Mplex(IMuxedConn):
     stream_queue: "asyncio.Queue[int]"
     next_stream_id: int
 
+    # TODO: `generic_protocol_handler` should be refactored out of mplex conn.
     def __init__(
         self,
         secured_conn: ISecureConn,
@@ -114,28 +117,25 @@ class Mplex(IMuxedConn):
         self.next_stream_id += 2
         return next_id
 
-    # FIXME: Remove multiaddr from being passed into muxed_conn
-    async def open_stream(
-        self, protocol_id: str, multi_addr: Multiaddr
-    ) -> IMuxedStream:
+    async def open_stream(self) -> IMuxedStream:
         """
         creates a new muxed_stream
-        :param protocol_id: protocol_id of stream
-        :param multi_addr: multi_addr that stream connects to
-        :return: a new muxed stream
+        :return: a new ``MplexStream``
         """
         stream_id = self._get_next_stream_id()
-        stream = MplexStream(stream_id, True, self)
+        name = str(stream_id)
+        stream = MplexStream(name, stream_id, True, self)
         self.buffers[stream_id] = asyncio.Queue()
-        await self.send_message(HeaderTags.NewStream, None, stream_id)
+        # Default stream name is the `stream_id`
+        await self.send_message(HeaderTags.NewStream, name.encode(), stream_id)
         return stream
 
-    async def accept_stream(self) -> None:
+    async def accept_stream(self, name: str) -> None:
         """
         accepts a muxed stream opened by the other end
         """
         stream_id = await self.stream_queue.get()
-        stream = MplexStream(stream_id, False, self)
+        stream = MplexStream(name, stream_id, False, self)
         asyncio.ensure_future(self.generic_protocol_handler(stream))
 
     async def send_message(self, flag: HeaderTags, data: bytes, stream_id: int) -> int:
@@ -181,11 +181,14 @@ class Mplex(IMuxedConn):
                     self.buffers[stream_id] = asyncio.Queue()
                     await self.stream_queue.put(stream_id)
 
+                # TODO: Handle more tags, and refactor `HeaderTags`
                 if flag == HeaderTags.NewStream.value:
                     # new stream detected on connection
-                    await self.accept_stream()
-
-                if message:
+                    await self.accept_stream(message.decode())
+                elif flag in (
+                    HeaderTags.MessageInitiator.value,
+                    HeaderTags.MessageReceiver.value,
+                ):
                     await self.buffers[stream_id].put(message)
 
             # Force context switch
@@ -200,14 +203,14 @@ class Mplex(IMuxedConn):
         # FIXME: No timeout is used in Go implementation.
         # Timeout is set to a relatively small value to alleviate wait time to exit
         #  loop in handle_incoming
-        timeout = 0.1
+        header = await decode_uvarint_from_stream(self.secured_conn)
+        # TODO: Handle the case of EOF and other exceptions?
         try:
-            header = await decode_uvarint_from_stream(self.secured_conn, timeout)
-            length = await decode_uvarint_from_stream(self.secured_conn, timeout)
             message = await asyncio.wait_for(
-                self.secured_conn.read(length), timeout=timeout
+                read_varint_prefixed_bytes(self.secured_conn), timeout=5
             )
         except asyncio.TimeoutError:
+            # TODO: Investigate what we should do if time is out.
             return None, None, None
 
         flag = header & 0x07
diff --git a/libp2p/stream_muxer/mplex/mplex_stream.py b/libp2p/stream_muxer/mplex/mplex_stream.py
index 2ec23f1..e90a1d4 100644
--- a/libp2p/stream_muxer/mplex/mplex_stream.py
+++ b/libp2p/stream_muxer/mplex/mplex_stream.py
@@ -10,6 +10,7 @@ class MplexStream(IMuxedStream):
     reference: https://github.com/libp2p/go-mplex/blob/master/stream.go
     """
 
+    name: str
     stream_id: int
     initiator: bool
     mplex_conn: IMuxedConn
@@ -21,13 +22,16 @@ class MplexStream(IMuxedStream):
 
     _buf: bytearray
 
-    def __init__(self, stream_id: int, initiator: bool, mplex_conn: IMuxedConn) -> None:
+    def __init__(
+        self, name: str, stream_id: int, initiator: bool, mplex_conn: IMuxedConn
+    ) -> None:
         """
         create new MuxedStream in muxer
         :param stream_id: stream stream id
         :param initiator: boolean if this is an initiator
         :param mplex_conn: muxed connection of this muxed_stream
         """
+        self.name = name
         self.stream_id = stream_id
         self.initiator = initiator
         self.mplex_conn = mplex_conn
diff --git a/libp2p/utils.py b/libp2p/utils.py
index 9a1f0cb..a309064 100644
--- a/libp2p/utils.py
+++ b/libp2p/utils.py
@@ -1,9 +1,20 @@
-import asyncio
-import struct
-from typing import Tuple
+import itertools
+import math
 
+from libp2p.exceptions import ParseError
 from libp2p.typing import StreamReader
 
+# Unsigned LEB128(varint codec)
+# Reference: https://github.com/ethereum/py-wasm/blob/master/wasm/parsers/leb128.py
+
+LOW_MASK = 2 ** 7 - 1
+HIGH_MASK = 2 ** 7
+
+
+# The maximum shift width for a 64 bit integer.  We shouldn't have to decode
+# integers larger than this.
+SHIFT_64_BIT_MAX = int(math.ceil(64 / 7)) * 7
+
 
 def encode_uvarint(number: int) -> bytes:
     """Pack `number` into varint bytes"""
@@ -19,35 +30,29 @@ def encode_uvarint(number: int) -> bytes:
     return buf
 
 
-def decode_uvarint(buff: bytes, index: int) -> Tuple[int, int]:
-    shift = 0
-    result = 0
-    while True:
-        i = buff[index]
-        result |= (i & 0x7F) << shift
-        shift += 7
-        if not i & 0x80:
+async def decode_uvarint_from_stream(reader: StreamReader) -> int:
+    """
+    https://en.wikipedia.org/wiki/LEB128
+    """
+    res = 0
+    for shift in itertools.count(0, 7):
+        if shift > SHIFT_64_BIT_MAX:
+            raise ParseError("TODO: better exception msg: Integer is too large...")
+
+        byte = await reader.read(1)
+
+        try:
+            value = byte[0]
+        except IndexError:
+            raise ParseError(
+                "Unexpected end of stream while parsing LEB128 encoded integer"
+            )
+
+        res += (value & LOW_MASK) << shift
+
+        if not value & HIGH_MASK:
             break
-        index += 1
-
-    return result, index + 1
-
-
-async def decode_uvarint_from_stream(reader: StreamReader, timeout: float) -> int:
-    shift = 0
-    result = 0
-    while True:
-        byte = await asyncio.wait_for(reader.read(1), timeout=timeout)
-        i = struct.unpack(">H", b"\x00" + byte)[0]
-        result |= (i & 0x7F) << shift
-        shift += 7
-        if not i & 0x80:
-            break
-
-    return result
-
-
-# Varint-prefixed read/write
+    return res
 
 
 def encode_varint_prefixed(msg_bytes: bytes) -> bytes:
@@ -56,7 +61,7 @@ def encode_varint_prefixed(msg_bytes: bytes) -> bytes:
 
 
 async def read_varint_prefixed_bytes(reader: StreamReader) -> bytes:
-    len_msg = await decode_uvarint_from_stream(reader, None)
+    len_msg = await decode_uvarint_from_stream(reader)
     data = await reader.read(len_msg)
     if len(data) != len_msg:
         raise ValueError(