A PA28 PVT PLT ENTERS THE CLASS B OF STL TWICE WHILE ATTEMPTING TO CIRCUMNAV THE EASTERN INNER RING TOO CLOSELY E OF STL; MO.

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PRIOR TO TAKE OFF FROM CPS; I WAS ADVISED TO MAKE A L TURN OUT AFTER TKOF. I COMPLIED WITH THESE INSTRUCTIONS AND CONTACTED ST LOUIS DEP AT 1500 FT MSL TO REQUEST VECTORS IN ORDER TO FLY TO MY DEST NW OF ST LOUIS. MY INTENDED RTE WAS TO FLY AROUND THE EASTERN EDGE OF THE ST LOUIS CLASS B AIRSPACE AND I WAS GIVEN INSTRUCTIONS TO MAKE A R TURN ON A HEADING THAT WOULD ACCOMPLISH THIS. AT THIS POINT I WAS AT 1800 FT MSL AND 5-8 NM W OF CPS; SLIGHTLY W OF THE ST LOUIS ARCH. (I WAS ALSO ASSIGNED A SQUAWK CODE AT THIS TIME.) MY INTENT WAS; AFTER COMING OUT FROM UNDER THE PORTION OF CLASS B AIRSPACE WITH A FLOOR OF 2000 FT MSL; CLB TO 2000 FT MSL; 1000 FT BELOW THE 3000 FT FLOOR OF CLASS B AT THE NEXT STAGE. AFTER XING THE RIVER IMMEDIATELY N OF THE ST LOUIS ARCH (MY CHK POINT FOR THE CHANGE IN AIRSPACE FLOORS) I CLBED TO 2000 FT MSL. I WAS THEN INFORMED THAT I NEEDED TO DSND TO BELOW 2000 FT IN ORDER TO STAY OUT OF CLASS B AIRSPACE. AT THIS POINT I BELIEVED I WAS CLR OF CLASS B; BUT COMPLIED BY DSNDING TO 1800 FT MSL; AS LOW AS I FELT COMFORTABLE CONSIDERING GND OBSTRUCTIONS; I CONTINUED ALONG THE E SIDE OF THE MISSISSIPPI RIVER ON VECTORS SUPPLIED BY ATC; MAINTAINING 1800 FT MSL. ROUGHLY 8-10 NM NW OF NICHOLS PVT ARPT ATC AGAIN MADE REF TO STAYING BELOW 2000 FT MSL TO CLR CLASS B AIRSPACE AND THAT I WAS ROUGHLY AT THAT ALT. THE VECTORS PROVIDED TO ME TOOK ME 5 MI W OF ST LOUIS REGIONAL (ALN) AND THEN NW; OUT OF ST LOUIS CLASS B AIRSPACE. AT THAT TIME I PROCEEDED ON HEADING TO MY DEST OF FFL. TO MY KNOWLEDGE AT NO TIME DID I MADE AN UNAUTH ENTRANCE INTO CLASS B AIRSPACE. MY ONLY POSSIBLE ERROR WAS FLYING TOO CLOSE TO THE CLASS B; BUT CONSIDERING THE GND OBSTACLES; THERE WAS LITTLE CHOICE.