ActionScript 2.0 :: Platformer - Character Clips Landing From Jump

I'm trying to make a platformer and I'm having a problem where the character will clip half through the ground upon landing from a jump. Just so you have a clear picture -- right now all that's on the stage is the character (which the code is placed in) and the ground (a completely flat plane called 'ground')

Here's the code:
onClipEvent(load) {
jumpHeight =0;
defaultJumpSpeed = 20;
jumpSpeed = 20;
} onClipEvent(enterFrame) {
[Code] .....

Right now the character's jump constantly decreases to give the effect of gravity. It starts out positive (character moves up), then goes negative (character falls down) The character will only stop falling if they come in contact with the ground (in the form of a hit test). The problem (I think) is that the character can fall at, say, 36 pixels a second or more, so sometimes they'll be half through the ground before the hit test goes off and stops him from falling further. How do I stop it without making the character fall-rate really, really low.