MD80 FLT CREW CLBS THROUGH ASSIGNED ALT; BECAUSE OF INCORRECT READBACK AT DFW.

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CLBING THROUGH APPROX 24500 FT; ATC CTLR ON ZFW CALLED AND SAID WE WERE ONLY CLRED TO FL230. WE RESPONDED THAT WE HAD BEEN CLRED TO FL290; IT HAD BEEN CONFIRMED BY BOTH CAPT AND FO; ENTERED IN THE ALT WINDOW AND POINTED OUT AS PER COMPANY PROCS; AND READ BACK TO ATC. HE STATED NEGATIVE; THAT WE HAD BEEN ASSIGNED AN AIRSPD OF 290 KTS. WE NEEDED 280 KTS FOR TURB AND HE HAD SAID MAINTAIN 280 KTS. WE THOUGHT WE HAD BEEN CLRED TO FL290. HE THEN CLRED US TO FL310. THERE OBVIOUSLY WAS AN UNINTENTIONAL MISUNDERSTANDING REGARDING THE 290 SPD AND CLRNC TO FL290. THE CAPT ASKED IF THERE HAD BEEN A CONFLICT AND I BELIEVE HE SAID POSSIBLY. THEN LATER ON THE SAME FREQ; WE WERE ASKED TO CALL ZFW ASAP BECAUSE THERE HAD BEEN A CONFLICT. THE FLT CONTINUED NORMALLY TO LGB AND THE CAPT CALLED THE ABOVE PHONE NUMBER AND INITIALLY SPOKE WITH THE WATCH SUPVR; MR X; ABOUT THE INCIDENT; AND WAS LATER SWITCHED TO MR Y AT FT WORTH QUALITY ASSURANCE AND DISCUSSED THE SIT FURTHER. APPARENTLY WHEN WE READ BACK CLB TO FL290; MR Y STATED TO THE CAPT THAT THE CTLR MISSED THIS READBACK. THE CAPT EXTENDED HIS APOLOGIES REGARDING THE INCIDENT AND SAID THAT WE WOULD PAY CLOSER ATTN IN THE FUTURE. IN SUMMARY; I THINK THAT BOTH THE CAPT AND FO SHOULD HAVE LISTENED MORE CLOSELY TO OUR ATC CLRNCS. BOTH PLTS HAVE LEARNED A VALUABLE LESSON REGARDING THE IMPORTANCE OF READBACKS AND HEARBACKS.