B757-200 CREW AND A CESSNA HAD A TCASII RA DEPARTING LGB.

Narrative

TCASII RA. TCASII RA WAS UNNECESSARY AND AVOIDABLE. DEPARTING LGB RWY 30; DEP CLRNC WAS 'RWY HDG 300 DEGS TO 1500 FT.' THEN 'L TO 180 DEG HDG CLB TO 2000 FT.' COMPANY PAGES REQUIRE NOISE ABATEMENT CLB USING MAX PWR -- V2 +10 KT CLB; AND MAX RATE INITIAL TURN 25-30 DEG BANK ANGLE. THIS PROFILE IS VERY BUSY AND RAPID. AFTER TKOF AS PLTS FOLLOWED DEP CLRNC; CAPT SPOTTED TFC AT SIMILAR ALT CLBING OUT OF LGB. AS WE CONTINUED TO 180 DEG HDG AND LEVELED AT 2000 FT MSL; THE LIGHT CESSNA TFC CONTINUED TO CLB THROUGH 1500 FT. (TCASII TA INDICATED -700 CLBING AT 2 MI LATERAL.) THE 180 DEG HDG WAS ON A COLLISION COURSE WITH THE CESSNA. AS CLOSURE RATE INCREASED TO -500 FT AND 2 MI; OUR SPD WAS 160 KTS. CAPT ELECTED TO CLB SIMULTANEOUSLY WITH TCASII RESOLUTION 'CLB; CLB' 1500 FPM -- AT THAT VERY MOMENT -- ATC ORDERED US TO CLB TO 3000 FT. CAPT RESPONDED TO ATC 'ROGER; CLBING TO 2000 FT; TFC IN SIGHT ON OUR L.' THE CESSNA PASSED 300 FT BELOW AND 1/2 MI LATERAL SEPARATION PER TCASII INFO. THE SIT WAS HIGHLY UNCOMFORTABLE FOR THE PLTS AS NO INFO WAS PASSED TO US REGARDING THE FLT PATH OF THE CESSNA OR THE REASON FOR THE 2000 FT CAP IN OUR DEP. THIS EVENT COULD HAVE BEEN AVOIDED BY HOLDING OUR TKOF FOR 30 SECONDS OR ALLOWING OUR CLB TO 3000 FT IMMEDIATELY. ATC SHOULD BE AWARE OF THE MAX PWR PROFILE WITH V2 +10 KTS; 30 DEG BANK TURNS. THE B757 WILL BE AT 3000 FT WITHIN SECONDS AFTER TKOF AND IS A HIGH WORKLOAD FOR THE CREW TO BE RESTR TO LESS THAN 3000 FT. TFC CONFLICTS SUCH AS THE ONE DESCRIBED SHOULD AND CAN BE AVOIDED WITHIN THE ATA.