PLT'S PERCEPTION OF WHAT WAS EXPECTED FROM ATC'S POSSIBLY INCONSISTENT CLRNCS; AND FAILURE TO QUESTION ATC; LED TO XING RESTR DEV.

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I WAS ENRTE TO HOUSTON SW ARPT FLYING A DIRECT RTE TO EAGLE LAKE VOR ON A HDG OF 120 DEGS AT 7000 FT MSL. CONDITIONS WERE VMC AND I WAS ON AN IFR FLT PLAN. I HAD PREVIOUSLY BEEN CLRED BY ZHU TO FLY THE LISSE 3 ARR TO AXH VIA THE ELA 108 DEG RADIAL. AT APPROX XA15 AM NEAR THE INDUSTRY VOR; ZHU INSTRUCTED ME TO CROSS KENDY INTXN (PART OF THE LISSE 3 ARR) AT 4000 FT. I ROGERED THIS. APPROX 10 MIN LATER NEAR ELA VOR; ZHU INSTRUCTED ME TO CONTACT HOUSTON APCH. I CONTACTED HOUSTON APCH AND TOLD THE CTLR THAT I WAS WITH HIM AT 7000 FT. THE APCH CTLR CAME BACK AND ASKED ME MY CURRENT ALT. I AGAIN RESPONDED BY STATING; 'I'LL GET YOU LOWER IN ABOUT 10 MI.' I 'ROGERED' THIS STATEMENT AND REMAINED AT 7000 FT AWAITING FURTHER INSTRUCTIONS FOR A DSCNT. AT THIS POINT; I WAS PAST ELA VOR FLYING INBOUND TO KENDY INTXN ON THE ELA 108 DEG RADIAL. APPROX 5 MI FROM KENDY; HOUSTON APCH INSTRUCTED ME TO DSND TO 4000 FT AT WHICH TIME I REDUCED PWR AND BEGAN MY DSCNT AT 500 FPM. I CROSSED KENDY INTXN AT AN ALT OF APPROX 6000 FT. AT THIS POINT I TURNED INBOUND ON THE HOBBY (HUB) VOR 070 DEG RADIAL ON A COURSE TO INTERCEPT THE AXH LOC. APPROX 10 MI LATER AT XA30 AM LCL TIME; HOUSTON APCH INSTRUCTED ME TO DSND TO 2000 FT. THE CTLR ALSO TOLD ME TO CALL ZHU BY TELEPHONE AFTER I LANDED. HE TOLD ME THAT I WAS SUPPOSED TO HAVE CROSSED KENDY INTXN AT 4000 FT. I REPLIED THAT I HAD AWAITED APCH CTL'S INSTRUCTIONS TO DSND SINCE HE HAD PREVIOUSLY TOLD ME THAT HE WOULD GET ME TO A LOWER ALT IN A SHORT WHILE. THE HOUSTON APCH CTLR REPLIED ON THE RADIO THAT IT MIGHT HAVE BEEN HIS FAULT FOR NOT BRINGING ME LOWER SOONER. AFTER I LANDED; I CONTACTED ZHU BY TELEPHONE AND EXPLAINED THAT I HAD NOT CROSSED KENDY AT 4000 FT BECAUSE I WAS WAITING FOR HOUSTON APCH TO CLR ME TO A LOWER ALT. THE ZHU CTLR REPLIED THAT; REGARDLESS OF MY PERCEPTION OF ATC INSTRUCTIONS; I DID NOT HAVE THE AUTH TO FLY AT WHATEVER ALT I DESIRED OVER KENDY INTXN BECAUSE OF ALT RESTRS IN THAT AREA. IN MY OPINION; I THINK THAT HOUSTON APCH SHOULD HAVE BEEN AWARE OF THESE ALT RESTRS AND BROUGHT ME DOWN TO 4000 FT BEFORE KENDY INTXN. IT DID NOT OCCUR TO ME TO RELAY ZHU'S PREVIOUS CLRNC TO HOUSTON APCH WHO; IN MY UNDERSTANDING; HAS THE AUTH TO CHANGE CTR'S CLRNC INSTRUCTIONS ONCE I FLY INTO HIS (APCH CTL'S) AIRSPACE. I THINK THERE WAS A BREAKDOWN IN COM BTWN ZHU AND HOUSTON APCH WITH REGARD TO MY CLRED ALT.