While building an item elevator for a creeper farm I ran into an issue. I have a clock that toggles the dropper and a line of redstone above it that powers a piston (the piston moves a block that un-hides a skeleton for easy record farming). The space I was working in was cramped so I took on the challenge to make everything fit. The pictures show roughly how I came to solve the problem. The only issue is that the line that keeps the piston extended prevents the dropper from functioning.

When the above line is on the dropper stops firing. Once the above line is turned off it does not fire again until it receives two pulses. The first pulse does not fire the dropper no matter how long you wait. The second pulse will fire the dropper and it then continues to function like normal.