Unless your system is specially configured, under most situations 'nice' and 'renice' can only be used to slow down a process (make it behave more nicely, and give up its cycles). Root is the only user (or someone with root-like powers), who can increase the priority of a process to a level above its default value (in the scope of 'nice', giving it a lower 'nice' value).

Unfortunately, most systems are set up so that everything runs at the highest priority -- so you have to renice everything else that is running, and can't just tweek the one program. (some multi-user systems are set up differently, but I don't know of any OSes that come set up this way out of the box). But of course, if you renice the wrong stuff, that's actually needed by the OS, you can have bad things happen.

I'd say the way to go is hardware related ( faster disk, more memory, etc ), or reworking the program in question to deal with whatever the bottleneck is. If the system has been up for a while, a reboot before the process might help if anything leaked memory.