If your bass is peaking a lot, turn everything down, not just the bass. If you pull the volume down on everything the same way, the relative volumes will stay the same and so the overall sound should be the same. The easiest way to do this is to just pull down the fader on the master channel, not touching the individual channels.
If it "doesn't sound as mighty" then turn the volume on your computer or speakers up. Unless you're trying to go deaf, you should still have plenty of headroom available on your computer's soundcard or your speaker's own amps.
If your bass is peaking only a little bit, then you might get away with using a limiter with its threshold set just below 0db, so that it only catches stuff that exceeds 0db. Or you can use a clipper and simply lop off the stuff that goes too loud. Both of these introduce changes in the sound, so you really only want to use them with the thresholds set really high.
Other things you can do: slap an EQ or a filter on the bass, see if you can remove some of the subbass. Oftentimes these days people put in a lot more sub than they actually need, and those low, low frequencies add a lot of volume that humans can't actually hear.
See if your percussion is roughly the same frequency range as your bassline. If they're interfering, you're probably turning up the bass to try to make it audible over the percussion. What you'll need to do in this case is move bass or the percussion to a different frequency, or just turn down the percussion.
Use a sidechain compressor, so that the bass goes away when the kick hits; if you do this, you'll want to set the release so that it at least sounds like the bass was still playing fully during the kick, even if it wasn't; basically you're trying to make the kick act as a bass note, leaving in just enough bass during the kick to give it a tone but not enough to actually interfere.
The general rule for using compression when mixing is that it's great for fixing irregularly wandering volume, like from an acoustic instrument or vocals. If you're working with synths, however, there are usually better tools for fixing clipping problems. First is the volume fader on the master channel, followed by limiting or deliberate clipping. Then you look at the subbass, you look at the other instruments, and you screw around with EQ or sidechaining or just straight-up changing what the other instruments are doing.
Otherwise, compression isn't that great a fixing tool. It's great as a shaping tool, 'cause you can use it to increase volume at the expense of dynamics (which can include transients as well as general dynamic range), and you can use it to make a bunch of different instruments sound like they're at least playing in the same room together, and you can go nuts on the sidechaining if you're making house.
But using compression as a fixing tool takes a lot of skill, so in general I don't really recommend that people do it. Sure it's less harsh than limiting, but getting all the settings right without the compression being too obvious is really hard, whereas with limiting you at least can say "threshold at 0db" and be pretty much done with it..