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We demonstrated how to calculate J$_{sf}$ ( d ) if a theoretical J$_{c}$ ( B ) is available, but our re- sult is also technologically relevant for investigating the reason of the J$_{sf}$ decrease in coated conductors with thicker superconducting layers. For such an analysis J$_{c}$ ( H ) should be mea- sured on the thinnest sample, where substrate interface effects do not play a role anymore. From this data J$_{c}$ ( B ) is determined down to inductions of about B$_{f}$ of the thinnest film. The remaining uncertainty in J$_{c}$ ( B ) (we suggest to assume a constant J$_{c}$ ( B ) at inductions below B$_{f}$ if no theoretical model is available) will introduce only a minor error in calculating J$_{sf}$ ( d ) for thicker films, provided they carry higher sheet current densities and thus elevate B$_{f}$ above the value of the thinnest film. 

We wish to emphasize, that the effect of the self-field is not an alternative explanation for a thickness dependent critical current density and will always be present, if the critical current density depends on the magnetic induction. A depression of J$_{sf}$ ( d ) significantly different from that calculated from J$_{c}$ ( B ) is thus indicative of an additional mechanism, such as a change in the material or pinning properties with thickness, determining the performance of the thicker conductor. If, however, the calculated and the measured J$_{sf}$ ( d ) are similar, the self-field controls the thickness dependence. In this case an improvement in 

