CAPT OF A WDB ACR ACFT WITH A SUSPECTED FLAT MAIN WING LNDG GEAR TIRE ALLOWED THE ACFT TO PREMATURELY DSND BELOW INITIAL APCH ALT.

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THOUGHT THAT THERE WAS POSSIBILITY OF A DEFLATED L WING TIRE AND HAD INFORMED MY COMPANY APPROX 6 HRS EARLIER. COMPANY HAD APPARENTLY WARNED TWR AND APCH CTL AND EMER EQUIP WAS STANDING BY. EXTENSIVE VECTORING WAS DONE SO THAT PRESUMABLY EMER EQUIP COULD BE POSITIONED. WAS ON APPROX 10 MI BASE TO FINAL FOR RWY 1 AT SDF AND HAD PREVIOUSLY BEEN ASSIGNED 4000 FT AND TO INTERCEPT THE LOC. MY FLT WAS LEVEL AT 4000 FT AND TFC WAS CALLED TO US AT 12 O'CLOCK AND 2800 FT NBOUND (A LNDG ACFT THAT WE WERE TO FOLLOW). ACFT WAS SIGHTED AND THEN NOTICED THAT MY ALT WAS 3800 FT AND DSNDING. STOPPED DSCNT AT 3700 FT AND INITIATED CLB BACK TOWARDS 4000 FT. SOME TIME DURING THESE EVENTS; WE WERE CLRED FOR VISUAL APCH FOLLOWING THE AFOREMENTIONED TFC. I BELIEVE THE CLRNC WAS AT SUCH CLOSE PROX TO THE TIME THAT WE WERE CLRED FOR THE VISUAL THAT THERE WOULD BE NO OFFICIAL CONCERN FOR AN ALT BUST. NOTHING WAS MENTIONED ABOUT ALT TRANSGRESSION BY THE CTLR. FLT WAS HANDED OFF TO TWR AND THE REMAINDER OF THE FLT WAS UNEVENTFUL. IN RETROSPECT; I LEFT THE 4000 FT EARLY AFTER HAVING SEEN THE TFC; BUT PROBABLY HAD NOT BEEN CLRED TO DO SO FOR A PERIOD OF SEVERAL SECONDS.