Avoiding unintentional harmonics?

[Tupac]

I like jam around near the ballpark of the 7th fret most of the time. But the problem is, that area is THE harmonic hotspot for the bass. I have a really hard time playing cleanly there because I just can't wrestle it to not give harmonics when I lift up on my left hand. How do I fix this?

 

[FrednBass]

Mute the strings with your left hand. Yes, the fretting hand.

 

[Tupac]

Mute the strings with your left hand. Yes, the fretting hand.

It doesn't work! I can lay all the fingers across but there's still that darn harmonic still ringing. The only way to avoid it is to spread them way out while pressing. Say I were to fret the 5th fret and pull up, even though I'd be covering the string with all my fingers, it still rings slightly.