It is well known that the large round trip time and the highly variable delay in a cellular network may degrade the performance of TCP. Many concepts have been proposed to improve this situation, including performance enhancing proxies (PEPs). One important class of PEPs are split connection proxies, which terminate a connection from a server in the Internet in a host close to the Radio Access Network (RAN) and establish a second connection towards the mobile User Equipment (UE). This connection splitting can be done either purely on the transport layer (TCP proxy) or on the application layer (HTTP proxy in the case of web traffic). While it is clear that an application layer proxy also infers the splitting of an underlying transport layer connection, the performance of applications may be essentially different for both approaches. In this paper, we first study the general impact of a split connection proxy on TCP bulk data transfer. We then focus on the case of web traffic and investi...