A great approach to Jazz Comping is to not only rely on chords but also use intervals as a way of conveying the harmony. Using intervals is an easier way to leave more space for the rest of the band, so it also works well if you play with a piano player.
In this video, I am going to go over some of the ways you can work with intervals and demonstrate how this works on the Jazz Standard All The Things You Are.
Finding intervals for Jazz Comping
If we first take a look at the first chord of All The Things: Fm7.
The note that we want to have in there is the 3rd and then add another note and check out the intervals we get, as shown here below:

Notice that I am not trying to find all options, just exploring and experimenting with what I think might work.
Voice-leading intervals
As an example, we can now look at how to voice-lead the different intervals on Fm7 to the next chord Bbm7. This could be done as shown in example 2.
In some of the examples I am adding extra movement between the two intervals. This is not too difficult when working with intervals so it is a good idea to already experiment with that option.

Counter melodies and polyphony
The final bars contain a few examples of several voices moving. In the last bar the voices are also moving in the opposite direction.
Playing the song with the intervals
When I comp like this I am not always staying completely clear with all chords, but I am trying to get an over all flow that makes sense on the song.
In this example I am keeping it simple by not having to many moving melodies and playing one or two intervals per chord.

Making an improvised Counterpoint as an exercise
You can turn the voice-leading part of this into a small counterpoint exercise that sounds like the one in the example below.
You can hear in the video how this example has a lot of moving voices, keeping one voice static while the other is moving around more.

Adding some rhythm and a little more Jazz Feel
Besides working on this with playing long notes and sustained sounds, you also need to work on using the intervals while adding some jazz rhythms.
An example of this is shown here below where there is also a focus on rhythm, not only moving voices, notes and extensions.

Get a free E-book
If you want to download a Free E-book of 15 II Valt I licks then subscribe to my newsletter:
Get the PDF!
You can also download the PDF of my examples here:
Jazz Guitar Insiders Facebook Group
Join 600+ Other Jazz Guitarists 🎸Join us in the Facebook Jazz Guitar Group Community: http://bit.ly/InsidersFBGroup
If you have any questions, comments or suggestions for topics then please let me know. Leave a comment on the video or send me an e-mail. That is the best way for me to improve my lessons and make them fit what you are searching for.
Please subscribe to my YouTube channel and feel free to connect with me via Instagram,Twitter Google+ or Facebook to keep up to date with new lessons, concerts and releases.