Starter goes "click" a few times, then works great

[davepl]

Long story short, I have a new LS3 with a new GM starter and solenoid. Battery seems fine.

Often when I go to start it, I get "Click". Nothing else.

Try again, "Click!"

Try again, "Click!"

Try again, "Crank-Start-Vroom!"

It -sounds- like a low battery situation, other than being a single click, but things seem charged up fine. When it finally does crank, it cranks fast.

I have ample grounds, I know that, as I even added extra braided straps. Positive cable to the battery isn't tight, but it's not doing the "arc at the cable and then stop working" thing.

Do LS solenoids act like this on the way out? Right now I'm just doing the "try it again" approach and it's always started, but one of these stays I assume it's not going to.

Diagnosis?