Minecraft – How to make this redstone staircase more compact

There are 3 designs in mind:

and also this

The third design is slowest but it is also the smallest,

While Ronan's answer will probably suffice in this situation, it will not be completely accurate. If you want a device that will pulse exactly 10 times, you can create a sort of counter with pistons. Here's the basic design:

This device uses a set of pistons to pulse a set number of times, then stop. Here's what the piston device looks like:

The glass block does not conduct redstone power, so the repeater does not power "through" it. All the stone blocks do conduct power, though, so those will be powered by the repeater. The pistons are set up to cycle through the blocks once the system is started, and it will stay on until the glass block becomes active.

These are the device's input and output. The lever overrides the glass block and turns the device on. The redstone line on the left will then pulse exactly 10 times before stopping. Note that the device will not stop if the lever remains on, so it might be a good idea to hook up a pulse limiter/extender to the input to keep the machine from malfunctioning.

Additionally, the speed of the pulses are determined by the clock seen in the first picture. By changing how fast the clock moves, you can adjust how often the output pulses. Note that I used all 1-tick repeaters to keep the length of the tick at about 2 redstone ticks, not extended to 4. If you're making it run more slowly, though, that's not necessary.