ALT OVERSHOOT DURING DEP FROM LAS VEGAS; NV. ATTRIBUTED TO DISTRS BY THE FLC.

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ON DEP FROM LAS VEGAS; WE HAD DEPARTED FROM RWY 1R; LNAV DEP WAS NOT IN EFFECT; THE DEP CLRNC WAS VECTORS AFTER TKOF. I WAS HAND FLYING THE ACFT WITH THE HUD DOWN. I BELIEVE OUR INITIAL HDG AFTER TKOF WAS A R TURN TO 050 DEGS; ALT CLRNC OF 7000 FT. WE WERE GIVEN A HDG CHANGE TO 070 DEGS; THIS PROBABLY OCCURRED ABOUT 6000 FT. THE ACFT; BEING A -700; AND RELATIVELY LIGHT WT; WAS CLBING AT A SOMEWHAT RAPID RATE. AS WE APCHED WHAT SHOULD HAVE BEEN MY LEVEL OFF ALT; WE BEGAN TO ENTER IMC CONDITIONS. I STATED; AND THEN PUT THE ENG ANTI-ICE SWITCHES ON. IT WAS DURING THIS PROC THAT THE ALT ALERT HORN SOUNDED AS WE WERE GOING THROUGH 7400 FT. I IMMEDIATELY REDUCED THE THRUST AND REVERSED THE CLB DIRECTION. OUR ALT REACHED 7600 FT BEFORE I BEGAN A DSCNT BACK TO 7000 FT. DEP CTL DID NOT COMMENT ON OUR ALTDEV; AND THERE DID NOT APPEAR TO BE ANY TFC CONFLICT -- NO TCASII WARNINGS WERE SOUNDED OR INDICATED. THE REMAINDER OF THE FLT PROCEEDED UNEVENTFULLY. I BELIEVE THAT THE PRIMARY FACTOR CONTRIBUTING TO THIS DEV WAS THAT ABOUT THE TIME THAT THE ALT ALERT SOUNDED FOR THE 1000 FT CALL; WE RECEIVED A HDG CHANGE FROM ATC. COMBINED WITH THEN ENTERING AN AREA OF PRECIP AND MY PREOCCUPATION WITH GETTING THE ANTI-ICE SWITCHES ON; MY CONCENTRATION WAS DIVERTED FROM LEVELING OFF. AN OBVIOUS CORRECTION THAT WOULD HAVE PREVENTED THIS OCCURRENCE WOULD BE HAVING THE AUTOPLT ON. THAT WOULD HAVE ELIMINATED THE NEED FOR ME TO LEVEL OFF.