I wired a new dimmer switch in a new addition room to three recessed lights. Each of the three lights has its own wire coming from the dimmer switch box (they are not wired in a circuit) The dimmer switch box is wired like this:

- power in to dimmer switch box
- Black power connected to dimmer switch bottom terminal, top switch terminal jumped/connected to 3 black light wires
- White power connected to three white light wires
- all grounds connected

The problem I'm having is when I first turn on the dimmer switch the light bulbs will immediately surge to full brightness and then quickly reset to whatever the (lower) dimmer setting is. Is this a problem? Did I wire it wrong someway? Thanks.

Did I wire it wrong someway?
Doesn't sound like it.
What is the make and model of dimmer switch. In the past dimmer were just adjustable resistors that didn't care how they were hooked up. These days who knows what kind of electronics are in them. You might try reversing the wiring. Also check wiring instructions.
What kind of bulbs are you using?

Thank you for responding. The bulbs I'm using are Utilitech 5-Watt (35W Equivalent) Mr16 Gu10 Pin Base Warm White Dimmable LED Spotlight Bulbs. The switch is a Cooper Wiring Devices Skye 8-Amp White Slide Dimmer. All bought at Lowe's. When you say reversing the wiring do you mean swapping out the black wire connections on the back of the switch? If so, I tried that and no difference. I'm thinking of just going back to Lowe's and buying a higher end (more expensive) switch and see what happens. The wiring to the dimmer switch box comes off a GFI receptacle. The GFI receptacle is wired to a underground wire/box that goes from the house to a small outbulding, which has it's own subpanel.

I have recently installed a similar dimmer at my son's house. When you turn the switch on, the same thing occurs, bright and then back to set point. Most likely a solid state setup. Look at the switch back, his said Line and Load.

Okay. I connected the hot incoming black to the Line (black screw) and the outgoing black to the Load/lights (gold screw). So do you think this is not a problem? The surging to full power when turning it on won't maybe blow the bulbs, or reduce their life? Think is should still be replaced with something other than solid state ?

hot incoming black to the Line (black screw) and the outgoing black to the Load/lights (gold screw).
That would be correct. It the dimmer is marked with LINE and LOAD then it makes a difference which way it is connected.

Suspect that the switch is either not compatible with LED lights or the surging is just a characteristic of the dimmer switch.

PS
Pull up you dimmer switch. Under its description it list.

Preset feature allows you to return to previous light level
I suspect that means that it comes on full brightness and then returns to the dimmer setting. In other words that is just how it operates. I would look for another brand dimmer.