Corporate aircraft flight crew missed crossing restrictions while on SLC PECOP2 SID. The Captain indicated ATC SID amended instructions were unclear and the ATC notation of the SID chart is confusing.

Narrative

[We were] departing SLC via the PECOP2 departure; SID states maintain 230 KTS and has various step climbs to 15;000 FT. SID also states maintain 15;000 FT. Our initial clearance was to maintain 10;000 FT. After take off we contacted Salt Lake Departure and immediately our speed restriction was canceled; thereby changing the departure; and we were cleared to maintain 12;000 FT shortly there after. The first fix MOZEL has a restriction of 10;000 FT or below with (ATC) printed in the restriction box on the SID chart. We passed MOZEL at about 11;000 FT. Our next clearance was to maintain 15;000 FT and to expedite our climb. We did and were thanked by ATC. We were then handed off to Salt Lake Center and cleared to FL230 prior to the fix DEZRT. DEZRT has a restriction of 15;000 FT or below. When we were cleared to FL230 we were at least 20 miles from DEZRT. As cleared by ATC we climbed to FL230 leaving 15;000 FT prior to DEZRT. No issue was made of this by ATC; often times ATC amends or changes SIDs. This was a confusing situation; no one mentioned 'climb via the departure' or 'cross x intersection.' We adhered to the ATC clearances we received. I wish we would have questioned ATC or ATC would have had clearer instructions regarding the procedure.