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One thing you could do if there's not a lot of other wireless networks around, is to set both the router and repeater to high-throughput mode, which more than doubles your bandwidth, hence giving you the "Up to 150mbps" speed labelled on the repeater. I'm not actually sure if the Bebox supports it though, if not the only way to get better speed is to buy a better repeater, or best of all, run an ethernet cable between the two.

I would personally also stick with the snappier browsing too, since then you could always plonk the device closer to the main router for faster downloads when you need them.