Jon and Phaedrus are right. But going into a little more detail...
It's not so much a wire issue as a burr issue. How do I know? If you were sharpening a wire, your knives would feel and act very sharp when they were fresh off the stones then dull quickly.
You can understand why I know you're getting a burr if you visualize the cross section of an ideal edge as a V; and then imagine the wire and burrs as tails which extend beyond the apex where the bevels meet with the cross section of a wire edge as a Y, and the cross section of a burr edge as a y.
Most likely you're rolling the edge on your finest stone and actually blunting it slightly. This can result from either creating a burr (y) or simply polishing the teeth off the edge you got from your coarser stone without creating a finer, fresh metal edge with your fine stone. The cross section of that edge would look something like a U.
Your steel not only straightens out (aka trues) the edge, but puts some scuff on it. At the apex where the edge bevels meet the scuff acts as micro-serration which -- depending on how you use sharpening terminology -- makes the knife more efficient (what I call perceived sharpness), but not actually sharper (absolute sharpness).
On the two bases of (1) improvement after steeling; and (2) the problem is more noticeable with your stronger knives more than your tougher ones, I'm also fairly sure that you're getting a very small burr which can be trued to create a good edge, as opposed to requiring an immediate deburring. Not that deburring -- getting rid of the tail on the y so the edge becomes a V -- wouldn't solve the problem as well.
The solution to the problem is a combination of better angle holding, better burr detection, more complete chasing, and more thorough deburring. In other words, you've got to break down your sharpening process and improve every step. If you're not using The Magic Marker Trick at this stage of your sharpening competence you should be.
It would be very helpful for my understanding of your process if you could describe to me how you check for a burr or wire; then describe how you chase and deburr it.
Finally, I urge you to ask a lot of questions to make sure you understand the process of creating burrs, detecting them, chasing them, and deburring. There are several people on this board who are excellent resources when it comes to sharpening.
Edited by boar_d_laze - 12/31/12 at 10:00am