NMAC.

Narrative

ON DEPARTING PARSONS IN 'OM1' RWY 33 CONTACTED ZME FOR IFR CLRNC ON 125.85 TO REQUEST CLRNC TO SPIRIT OF ST LOUIS IFR. MEMPHIS INSTRUCTED ME TO SQUAWK 1511. I ENTERED SQUAWK CODE INTO XPONDER AND WHEN I LOOKED UP I SAW I WAS ON COLLISION COURSE WITH 'C17' HEADING 060 DEGS AT 2500 FT MSL. IMMEDIATELY NOSED PLANE OVER AND TURNED TO R TO AVOID COLLISION MIDAIR. PLT OR COPLT OF MIL TRANSPORT THEN CONTACT ZME 125.85 AND NOTIFYING THEM OF HAVING TO CLB TO AVOID NEAR MISS WITH PIPER OR SOME TYPE OF SMALL ACFT AND REQUESTING CTR TO DO A BETTER JOB OF CALLING OUT RADAR TARGETS. ZME INFORMED THE TRANSPORT THEY WERE BELOW RADAR COVERAGE AND THAT ACFT WAS PROBABLY BONANZA CLBING OUT OF PARSONS. I NOTIFIED CTR THAT I WAS IN FACT THE ACFT INVOLVED AND THAT I HAD DSNDED TO AVOID A COLLISION. TO AVOID THIS SIT IN THE FUTURE ONE SHOULD ALWAYS CLR THE AREA VISUALLY BEFORE ATTENDING TO COCKPIT CHORES. ATC SHOULD HAVE KNOWN THE C17 APPROX POS THAT WAS IN MY VICINITY; AND ALERTED EITHER OR BOTH ACFT TO BE ALERT FOR POSSIBLE CONFLICT. AS THE AIRSPACE WAS NOT A MOA OR RESTR THE MIL AND ATC SHOULD PROHIBIT SUCH LOW LEVEL FLTS AND HVY JET ACFT IN NON RADAR ENVIRONMENTS.