CAPT OF A DC9 OVERSHOT INTERMEDIATE ALT AFTER TKOF AT DCA DUE TO HVY WORKLOAD OF COMPLYING WITH DEP CTLR'S LAST MIN CHANGES.

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CHANGED RWYS BECAUSE OF WIND CHANGE CAUSED BY RAINSHOWERS TO THE NW OF THE ARPT. WHILE IN POS AND HOLD ON RWY 1; DECIDED WE COULD MAKE AN EASTERLY DEP. OUR CLRNC WAS CHANGED FROM THE NW DEP AND CLB TO 5000 FT; TO A R TURN 090 DEGS AND CLB TO 2000 FT. IMMEDIATELY AFTER TKOF; TURNED TOWARD 090 DEGS; AND GIVEN ANOTHER TURN TO 110 DEG HDG TO AVOID THE PROHIBITED AREA. AS ROLLING OUT ON THE 110 DEG HDG; TWR GAVE US A TURN TO 040 DEGS; BACK TOWARD THE WX AND THE FREQ CHANGE TO DEP CTL. IT WAS DURING THE TURN AND THE FREQ CHANGE (I HAD MY HEAD DOWN CHANGING THE FREQS) THAT WE WENT ABOVE 2000 FT BY ABOUT 400 FT BEFORE RETURNING TO 2000 FT. OBVIOUSLY WE WERE CONCERNED WITH FLYING INTO THE RAINSHOWERS; AND THE LAST SECOND CLRNC CHANGE WERE FACTORS; BUT THE MOST DISTRACTING THINGS WERE THE SECOND HDG CHANGE RESULTING IN A ROLL FROM A 25 DEG R BANK TO A 25 DEG L BANK; AND THE FREQ CHANGE JUST PRIOR TO 2000 FT. THE CTLR SEEMED MORE WORRIED ABOUT THE PROHIBITED AREA AND OTHER AIRSPACE THAN TURNING US INTO THE RAINSHOWERS.