B737-300 ACKNOWLEDGED CLRNC TO TURN 230 DEGS DIRECT MEI VOR WHEN ABLE CLB 13000 FT. FREQ CHANGE TO ZTL BUT NO CONTACT. OUT OF 10000 FT BACK ON DEP FREQ CTLR ADVISED TO MAINTAIN 10000 FT THE CLRED ALT. WAS AT 10600 FT AND RETURNED TO 10000 FT. NO CONFLICT.

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TOOK OFF FROM BHM RWY 5 AND HANDED OFF TO DEP CTL. ON INITIAL CONTACT WE TOLD HIM WE WERE CLBING TO 5000 FT. DEP TOLD US TO TURN R TO 230 DEGS AND GO DIRECT TO MERIDIAN WHEN ABLE; AND WE UNDERSTOOD HIM TO SAY CLB TO 13000 FT. WE READ BACK THE TURN AND THE CLB TO 13000 FT. HE TOLD US TO CALL ZTL ON 132.25. WE TRIED TWICE TO CONTACT HIM WITH NO RESPONSE; SO RETURNED TO BHM DEP CTL. WE WERE THEN CLBING OUT OF ABOUT 10600 FT. HE TOLD US TO MAINTAIN 10000 FT. WE SAID WE WERE ALREADY THROUGH 10000 FT AND HE SAID ALL WE WERE CLRED TO WAS 10000 FT. HE SAID TO TRY ATL AGAIN; WHICH WE DID AND GOT HIM ON OUR FIRST CALL. HE CLRED US HIGHER AND WE CONTINUED THE CLB. NO MENTION WAS MADE OF ANY OTHER ACFT IN THE AREA; AND WE HAD NO TARGETS ON THE TCASII. WE WERE VERY LIGHT AND CLBING VERY RAPIDLY. I FEEL THAT IF WE'D HAVE HEARD 'ONE ZERO; TEN THOUSAND' THAT THERE WOULD HAVE BEEN NO MISUNDERSTANDING THE VERBIAGE. ALSO; WE READ BACK 'ONE THREE THOUSAND' AND WERE NOT CORRECTED ON IT; SO WERE VERY CONFUSED UPON RETURNING TO DEP AND HEARING THAT WE'D ONLY BEEN CLRED TO 10000 FT.