[quote="FrankM"]I'll go w/ lousey right hand technique. : ^)
If you ensure that your fingers are comming from underneath the strings, instead of down onto of the strings when you play, it will clean up your sound.
I know this is an older post but... I've read (in Bass Playing for Dummies and others) and seen that many pros believe that the ONLY proper way to finger pick a bass string is to attack with the finger nearly parallel to the bass body, pushing the string in toward the pickups.

Opposite of what FrankM is saying to do. Personally, I agree with FrankM and play like Billy Sheehan does, with a more vertical (floor to ceiling) attack. It definitely allows for closer action.
Dummies goes so far as to demonstrate, on the cd, the SUPPOSED inferior tone from picking vertically. I have been playing this way since day one, nearly 20 years ago, and I've never been turned away from a band or music project. So, I guess my tones good

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BTW, playing near the bridge WILL help. But, you may have issues with the G string. I occasionally strike it TOO close to the bridge, since the bridge is tilted to accomodate the fanned scale. I'm a Dingwall newbie and I'm still adjusting.