To experimentally explore the influence of Lewis number Le, laminar flame thickness delta L, pressure P, and unburned gas temperature Tu on turbulent flame speed ST, a set of conditions is designed by adjusting nitrogen mole fraction in lean H-2/O-2/N-2 (Le=0.35) and stoichiometric CH4/O-2/N-2 (Le approximate to 1) mixtures. The adjustment is performed by simulating complex-chemistry laminar flames to obtain the same laminar flame speeds SL not only for different fuels, but also for different pressures (1, 2, and 5 atm). The mixtures are characterized by significantly different SL at Tu=300 K and 400 K, whereas variations in delta L with the temperature are sufficiently weak. Moreover, laminar flame thicknesses are approximately equal for H-2-based and CH4-based mixtures at the same P, but are significantly decreased with increasing pressure. For this set of conditions, ST is measured by applying schlieren imaging techniques to film expansion of centrally ignited, statistically spherical flames in homogeneous isotropic turbulence generated by a dual-chamber, constant-pressure, fan-stirred explosion facility. Analyses of the measured data show the following trends. First, turbulent flame speed is increased by both P and Tu, whereas ST/SL is decreased with increasing Tu. Second, turbulent flame speed measured at different P and Tu can be predicted by allowing for SL(P,Tu) and delta L(P,Tu). Thus, the present data do not call for explicitly substituting normalized pressure or temperature into a turbulent flame speed approximation. Third, ST is increased with decreasing laminar flame thickness. Fourth, speeds of the lean H-2/O-2/N-2 flames are higher when compared to the stoichiometric CH4/O-2/N-2 flames, with this difference is increased (reduced) by P (Tu, respectively). Fifth, all measured data on ST can quantitatively be described by substituting SL and delta L with the counterpart characteristics of highly strained twin laminar flames. The latter finding supports leading point concept of premixed turbulent combustion.