Pressure (P) derivatives of thermal conductivity (k) and thermal diffusivity (D) are important to geophysics but are difficult to measure accurately because minerals, being hard and partially transparent, likely incur systematic errors through thermal losses at interfaces and spurious radiative transfer. To evaluate accuracy, repeat experiments for olivine [(Mg(0.9)Fe(0.1))(2)SiO4], quartz (SiO2), and NaCl are examined in detail: these and other data on electrical insulators are compared with theory. At ambient conditions, D is underestimated in proportion to the number of contacts. As temperature (T) increases, spurious radiative transfer more than offsets contact loss. Compression of pore space and contact losses affect pressure derivatives, but these seem independent of T. Accurate (+/-2%) values of D(T) at 1 atm are obtained with the contact-free, laser-flash method. Other optical techniques do not pinpoint D but provide useful pressure derivatives. Published data on (partial differential)(lnk)/(partial differential)P at ambient conditions agree roughly with all available models, the simplest of which predicts (partial differential)(lnk)/(partial differential)P approximately (partial differential)(lnK(T))/(partial differential)P, where K(T) is the bulk modulus. However, derivatives verified by multiple measurements are reproduced accurately only by the damped harmonic oscillator model. An improved database is needed to refine this model and to confidently extrapolate these difficult measurements to geophysically relevant conditions.