An ablation electrode is mounted on the distal end of a catheter with a firstportion inside and a second portionoutside the catheter. The second portion is adapted to have a surface thatmakes maximum contact with a tissue to be ablated,leaving a minimum area not covered by the tissue and potentially exposed toblood. The first portion is adapted to provide anex-tended surface area for efficient exchange of heat with a coolant flowinginside the catheter. Outlets provided near the area notcovered by the tissue in the second portion prevents blood from getting closeto or come directly in contact with the area, therebygreatly reducing formation of dangerous blood clots. The minimizing of anelectrical circuit through blood greatly reduces wastedpower into the electrode so that the efficiently cooled electrode is notburdened. The catheter preferably has multiple electrodeswith similar features.