This paper explores the design trade-offs needed for an Internet transport protocol to effectively support web access over HTTP/1.1. It explores use of a multistreaming transport protocol mechanism and studies these using a practical methodology utilising the transport features of TCP and SCTP. This is used to evaluate the relative benefit of key transport mechanisms and analyse how these impact web access performance. Our conclusions help identify the root causes of performance impairments and suggest appropriate choices when selecting a suitable transport protocol.