AN IFR PIPER SENECA PILOT ENCOUNTERED ICING DURING DESCENT AND APCH. IN VIOLATION OF HIS CLRNC HE DSNDED TO 2000 FT MSL TO MELT ICE.

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ON A FLT FROM ZZZ1 TO ZZZ; I WAS IN A PIPER SENECA I. THE RTE OF FLT WAS DIRECT AT 7000 FT MSL. CLOUD TOPS WERE AROUND 5000 FT MSL. I BROKE OUT OF THE CLOUDS WITH TRACE RIME ICE OUT OF ZZZ1. CTR CLRED DSCNT AT PLT'S DISCRETION TO 2800 FT MSL. I FOLLOWED A RATE OF AROUND 1000 FPM TO 2800 FT MSL. I PICKED UP MODERATE RIME ICE IN THE DSCNT. ONCE AT 2800 FT MSL ATC INFORMED ME TO CLB TO 3000 FT MSL. 3000 FT MSL IS THE MINIMUM ALT FOR THE APCH UNTIL 14 DME. I INFORMED ATC I WAS UNABLE TO STAY AT 3000 FT DUE TO THE ICE BUILDUP. THE ACFT HAD ACCUMULATED AROUND 1/8 - 1/4 INCH OF RIME ICE BY THIS POINT. I REQUESTED A DSCNT TO 2500 FT MSL TO GET TO WARMER TEMPS TO AVOID ADDITIONAL ICE BUILDUP. ATC ADVISED THEY COULD NOT ALLOW THAT LEGALLY. I WAS OUTBOUND TO VOR AT 2800 FT MSL AND THE ICE KEPT BUILDING. I INFORMED ATC I WAS UNABLE TO COMPLY WITH INSTRUCTIONS. THEY ASKED WHAT I NEEDED. I SAID; 'I WANT TO TURN 360 DEGS AND PROCEED INBOUND AT 2000 FT MSL (MDA FOR CURRENT SEGMENT).' I PERFORMED WHAT WAS STATED I WAS GOING TO DO. I FOLLOWED THE 144 DEG RADIAL OFF THE VOR INBOUND AND DSNDED TO 2000 FT MSL. AT THIS POINT THE ICE BEGAN TO MELT OFF THE LEADING EDGES AND WIND SCREEN. I LANDED WITH LESS THAN 1/8 INCH OF ICE ON ACFT. I DIDN'T REALIZE THE ICE WOULD BE BUILDING SINCE ZZZ1 WAS 2000 FT OVCST AT TIME OF DEP.