It is important to utilize the free stroke. Free stroke is when you do NOT rest your finger on the next string after you make the note. You curve your finger a bit more than you do with rest stroke and pull the tip away from the soundboard after you strike the string making sure you don't touch any other string than the one you've just plucked. The proper place of contact is still the left side of your finger where the nail meets the flesh (similar to rest stroke). The sound of free stroke is less loud and percussive than rest stroke, but the tonal quality should be the same. It's mainly used in arpeggios - for obvious reasons. It is also useful when you need to play melodic passages integrated into arpeggios. Since rest stroke requires some adjustment of the whole right hand position it is not always suitable to play complex passages that incorporate sequences that involve active bass and treble sections that go together. Take a look at the following video as an example for free stroke:
The key is to try and keep the right hand as steady as possible. The thumb and the fingers should move independently while you keep your wrist as steady as possible. I use the following short sequence I've made up to practise free stroke. Give it a try.