The steadily growing deployment of resilience-critical Internet services is leading to an increasing number of Multi-Homed network sites. Asymmetric Digital Subscriber Lines (ADSL) are an inexpensive way to add a secondary Internet access connection. With the development of Multi-Path Transport Layer protocols - like Multipath TCP (MPTCP) and the Stream Control Transmission Protocol (SCTP) furnished by a Concurrent Multipath Transfer (CMT-SCTP) extension - there is also a strong interest in utilising all access connections simultaneously to improve the data throughput of the applications. However, combining network paths over ADSL with paths over other access technologies like fibre optic links implies highly dissimilar paths with significantly different bandwidths, delays and queuing behaviours. Efficient Multi-Path transport over such dissimilar paths is a challenging task for the new Transport Layer protocols under development. In this paper, we show the difficulties of Multi-Path transport in a real-world dissimilar path setup which consists of a high-speed fibre optic link and an ADSL connection. After that, we present an optimised buffer handling technique which solves the transport efficiency issues in this setup. Our optimisation is first analysed by simulations. Finally, we also show the usefulness of our approach by experimental evaluation in a real Multi-Homed Internet setup.