Various types of high temperature superconducting single crystals (TI-2223, Bi-2212, and Y-123 with oxygen contents between 6.4 and 6.64) were investigated by SQUID magnetometry. Both materials show very {open_quotes}low{close_quotes} lying irreversibility lines (Hllc), which follow an exponential law-and rise rapidly below T/T{sub c}=0.5. High critical current P densities are found only at low temperatures, e.g. J{sub c} is about 2.7{circ}10{sup 10}Am{sup -2} at 1 T and 5 K in TI-2223. A comparison of the condensation energy provided by different types of defects with the thermal energy gives evidence for pinning of individual pancakes by the as-grown defect structure.