The atomic force microscope can detect the mechanical fingerprints of normal and diseased cells at the single-cell level under physiological conditions(1,2). However, atomic force microscopy studies of cell mechanics are limited by the 'bottom effect' artefact that arises from the stiff substrates used to culture cells. Because cells adhered to substrates are very thin(3), this artefact makes cells appear stiffer than they really are(4). Here, we show an analytical correction that accounts for this artefact when conical tips are used for atomic force microscope measurements of thin samples. Our bottom effect cone correction (BECC) corrects the Sneddon's model(5), which is widely used to measure Young's modulus, E. Comparing the performance of BECC and Sneddon's model on thin polyacrylamide gels, we find that although Sneddon's model overestimates E, BECC yields E values that are thickness-independent and similar to those obtained on thick regions of the gel. The application of BECC to measurements on live adherent fibroblasts demonstrates a significant improvement on the estimation of their local mechanical properties.