CE550 FLT CREW EXCEEDS 1500 FT PRIOR TO 4.5 DME DURING THE TEB 5.

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WHILE TAXIING I BRIEFED THE PF ON THE DEP PROC FOR RWY 24 (TEB 5). CLB TO 1500 FT MSL UNTIL 4.5 DME OFF TEB VOR; THEN 2000 FT MSL; THE PF DETERMINED THAT 2000 FT WOULD BE PUT INTO THE ALT ALERTER INSTEAD OF 1500 FT BECAUSE HE WOULD LEVEL IT OFF HIMSELF. WHEN CLRED FOR TKOF; WHILE TAXIING ONTO THE RWY; I BRIEFED THE PROC ONE MORE TIME TO THE PF AND WE DEPARTED ON THE SID; I WAS TEMPORARILY DISTRACTED WHILE CONTACTING THE DEP CTLR; AND WHILE CHKING IN AND GIVING HIM OUR POSITION AND ALT; I REALIZED THAT THE PF WAS GOING THROUGH THE 1500 FT MSL ALT RESTR AS WE WERE ONLY 3.0 DME FROM THE TEB VOR. THE CTLR RECOGNIZED THE SITUATION IMMEDIATELY. THE SITUATION WILL BE AVOIDED IN THE FUTURE BY PLACING ANY ALT RESTR IN THE ALERTER; AND ALLOWING THE AUTOPLT TO FLY THESE TIGHT ALT RESTRS.SUPPLEMENTAL INFO FROM ACN 739487: WE WERE REPOSITIONING FROM TEB TO PICK UP PAX. AS PART OF OUR NORMAL CHECKLIST THE CAPTAIN AND I REVIEWED THE TETERBORO 5 DEPARTURE WE HAD BEEN CLEARED FOR. FROM RUNWAY 24; IT'S A CLIMB TO 1500 FEET ON RUNWAY HEADING THEN A RIGHT TURN TO 280; MAINTAIN 1500 FEET UNTIL REACHING 4.5 DME THEN CLIMB TO 2000 FEET. AS THE PF I ELECTED TO SET THE ALTITUDE ALERTER TO 2000 FEET PRIOR TO TAKEOFF AND DECIDED TO HAND FLY UNTIL REACHING THAT ALTITUDE. SHORTLY AFTER TAKEOFF AND UPON REACHING 1500 FEET WE WERE INSTRUCTED TO CONTACT NY DEPARTURE. THE CAPTAIN DID SO AND I BEGAN A RIGHT TURN TO 280 AT 1500 FEET. BEFORE NY RESPONDED THE CAPTAIN; SEEING MY RIGHT TURN; SAID '2000 FEET;' WHICH I TOOK TO MEAN CLIMB TO 2000 FEET. WITHOUT THINKING ABOUT IT FIRST I BEGAN A CLIMB TO 2000 FEET. NY RESPONDED TO OUR CALL; VERIFIED RADAR CONTACT AND INSTRUCTED US TO FLY A HEADING OF 270. IN THAT SHORT TIME SPAN I REALIZED THAT IT WAS TOO EARLY TO CLIMB TO 2000 FEET AND LEVELED OFF WITH THE INTENT OF DESCENDING BACK TO 1500 FEET. AT THAT TIME WE WERE AT 1800 FEET AND NY CONTACTED US AGAIN TO LET US KNOW WE WERE NOT FOLLOWING THE DEPARTURE PROCEDURE CORRECTLY. I THINK THERE WERE TWO PROBLEMS THAT CONTRIBUTED TO THIS MISTAKE. THE FIRST WAS MY DECISION TO HAND-FLY THE AIRPLANE THROUGH THE DEPARTURE PROCEDURE. IN HINDSIGHT 500 VERTICAL FEET DOES NOT LEAVE MUCH ROOM FOR ERROR. IT WOULD HAVE BEEN SMARTER TO SET THE ALTITUDE ALERTER TO 1500 FEET AND LET THE AUTOPILOT FLY THE PROCEDURE. THE SECOND WAS THE CAPTAIN TRYING TO FLY THE PLANE FROM THE RIGHT SEAT. HE WAS BUSY ENOUGH WITH THE COMMUNICATIONS AND CHECKLISTS.