ALTDEV ALT OVERSHOT IN CLB.

Narrative

20 NM E OF SXC AND ON A FLT PLAN FILED TO FL280 -- PASSING FL200 IT WAS RPTED THAT FL240 WOULD BE A SMOOTHER RIDE. WE ACCEPTED FL240 AS A FINAL CRUISE ALT; HOWEVER PASSING FL230 THEY CLRED US DIRECT RZS. AS WE WERE TURNING; THE ACFT WENT THROUGH FL240 TO ANYWHERE BTWN FL243 AND FL244. WE IMMEDIATELY DSNDED AND LEVELED AT FL240. NOTHING WAS SAID BY ATC. NO WARNINGS IN THE COCKPIT WENT OFF. SUPPLEMENTAL INFO FROM ACN 305788: OUR ACFT IS A B-737-300 WITH FMS. DURING THE TRANSITION FROM VOR NAV TO LATERAL NAV FOR THE NEW FIX; THE COPLT FLEW ABOVE THE CLRED FL240 TO FL244. A RETURN TO CLRED ALT WAS ACCOMPLISHED. I THINK THIS DEV WAS CAUSED BY A FIXATION BY BOTH OF US ON SWITCHING THE FMS FROM VOR TO LNAV MODES. ALSO; WE NORMALLY CRUISE MUCH HIGH THAN FL240; BUT BECAUSE OF TURB WE WERE STAYING LOW. I THINK THAT I WAS USED TO CLBING FOR A LONGER PERIOD OF TIME AFTER CHKING IN WITH THE HIGH ALT SECTOR; THUS I DIDN'T REALIZE THAT WE WOULD BE LEVELING ALMOST IMMEDIATELY. I SHOULD HAVE PUT MORE AWARENESS ON THE VERT NAV; THERE WAS PLENTY OF TIME TO HANDLE THE LATERAL NAV AFTER LEVELOFF AT FL240.