ALTDEV ALT EXCURSION ALT OVERSHOOT.

Narrative

WE WERE CLRED SDL 4 DEP; RWY 3. AS THE DEP DEPICTED WE HAD TURNED TO A HDG OF 260 DEGS AND WERE CLBING TO 5000 FT AS CLRED. AS WERE LEVELING OFF AT 5000 FT THERE WAS A HOT AIR BALLOON JUST TO THE R OF OUR FLT PATH. THE CTLR GAVE US A R TURN TO 360 DEGS. AT THIS TIME OUR TCASII GAVE US A TA. THE FO LOOKED AT THE TCASII; WHICH AT THIS TIME WAS VERY CLUTTERED; AND VERIFIED A MINUS AMBER BALL; INDICATING A POSSIBLE CONFLICT AT 12 O'CLOCK BELOW US. LOOKING OUTSIDE; I COULD NOT SEE THE 12 O'CLOCK TFC; HOWEVER; IF WE MADE A TURN TO 360 DEGS; AS INSTRUCTED; WE WOULD BE IN DIRECT CONFLICT WITH A HOT AIR BALLOON ON OUR ALT. I THEN ADVISED DEP OF THE CONFLICT; AND STATED THAT WE NEEDED A HIGHER ALT TO CLR THE BALLOON. DEP INSTRUCTED US TO MAINTAIN PRESENT HDG UNTIL ABLE TO MAKE THE TURN. THERE WAS A LOT OF OTHER RADIO TFC INCLUDING ANOTHER GULFSTREAM; WITH CONFLICTING XMISSIONS; MAKING COMS DIFFICULT. I FELT THAT WE HAD BEEN CLRED TO A HIGHER ALT. AS WE PASSED THROUGH 5000 FT; I ASKED THE FO WHAT OUR NEW ALT WAS. HE SAID 5000 FT. I THEN ASKED DEP TO VERIFY THE ASSIGNED ALT. THIS TOOK SEVERAL XMISSIONS BECAUSE OF OTHER RADIO CONFLICTS. THEIR REPLY WAS FOR US TO DSND TO 5000 FT AND TURN TO 180 DEGS AND FOR ANOTHER ACFT TO TURN R. WE IMMEDIATELY COMPLIED WITH THIS INSTRUCTION. AT NO TIME WAS THE TFC; WHICH WAS ON OUR TCASII; DEPICTED AS A TA. THIS WAS ALSO VERIFIED BY THE FO WHO HAD THE TFC TO OUR R AND AT A HIGHER ALT IN SIGHT. THE TFC WAS CONFIRMED VISUALLY WHEN IT RESPONDED AT ATC'S COMMAND FOR A R TURN. THE REST OF THE FLT WAS COMPLETED UNEVENTFULLY. 1) IT WOULD PROBABLY HELP ATC IF HOT AIR BALLOONS OPERATING IN HIGH TFC AREAS HAD XPONDERS. 2) TO REINFORCE ALT LIMITS IT WOULD HELP IF ATC WOULD ALSO ALWAYS GIVE ALT LIMITS WITH ALL HDG AND/OR CLRNC CHANGES.