Although there are times when strong muscular exertion in the left hand may be beneficial, in general we want to use a minimal amount of effort. The fingers should press the string with only enough force to produce the note cleanly, and no more. Keeping minimum finger pressure in the left hand will help with speed, stamina, shifting, general ease of motion, and a host of other things.
To discover the what minimum pressure feels like, we can perform an exercise Mimi Zweig calls “Elevator Fingers.” The image is this:
Envision yourself traveling on a painfully slow elevator. You are going from the top floor of the building to the first floor. The elevator can continue on to the basement, but you are stopping at the first floor.
Now imagine your fingers as being that elevator and play the exercise below:
Note: This exercise is most effective when using the bow, but you can adapt it for pizzicato playing by plucking the string in a tremolo fashion with the right hand fingers. Press with the left hand only until you produce a pure tone. In general, pizzicato playing requires slightly more left hand pressure than does arco playing.
Start the exercise by very lightly touching the string. Use less pressure than you would use if you were playing a harmonic. Play with a slow bow, closer to the bridge than to the fingerboard. The bow should grip the string just as if the note were fully pressed. Playing the exercise in one bow is preferable, but you may change bows rather than rush the movement of the left hand fingers. Press the finger down very, very slowly. Your thumb will counter-press against the neck, but make it is only as much as needed and as little as possible. Keep both the thumb and pressing finger as light as possible. The unused fingers and their respective joints should remain relaxed and should not squeeze against each other, press against the string, or stiffen. If you notice tension elsewhere in your body, attempt to minimize it as well.
As you play the exercise. Feel and listen for the exact amount of pressure needed to stop the note well. Be forewarned: If you are doing this exercise correctly there will be times where the sound produced will be dreadful. Continue pressing, slowly, until you have stopped the note cleanly. Once you produce a pure tone, immediately stop the movement of your finger and hold the note. Once there, really feel how much pressure it takes to stop that note. Or, more likely, really feel how much pressure is NOT needed to stop that note.
Do this with all fingers, on all strings and in all areas of the bass. It is an excellent exercise to do with each and every note of a scale. You can also apply it to specific pieces, if you are having trouble with left hand tension in a particular section. Apply it to double, triple and quadruple stops to ensure you don’t lock up during these technical feats either. However you apply it, always set out to discover what minimum pressure feels like. Take you time with it and don’t be in a rush.