CATALYTIC CONVERSION OF PETROLEUM FEEDSTOCKS, SUCH AS THE CRACKING OF A GAS OIL IN A VERTICAL TRANSPORT REACTOR, IS IMPROVED BY EFFECTING RAPID SEPARATION OF CATALYST FROM REACTOR EFFLUENT AND REGENERATING CATALYST IN A MULTI-STAGE FLUID-BED SYSTEM. A HIGHER YIELD OF DESIRABLE PETROLEUM PRODUCTS AND A LOWER CARBON LEVEL ON SPENT CATALYST ARE REALIZED. PARTIAL REGENERATION OF SPENT CATALYST IS EFFECTED IN A FIRST DILUTE-PHASE REGENERATION STAGE, PERMITTING SUBSEQUENT USE OF A HIGH REGENERATION TEMPERATURE IN ORDER TO REACH AN ACCEPTABLY LOW CARBON LEVEL ON REGENERATED CATALYST WITHOUT HARM TO SENSITIVE CONVERSION CATALYSTS.