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A technique for testing the weak-equivalence principle is presented. This technique involves the measurement of differential accelerations between two test masses of different materials (e.g., aluminum and gold) free falling inside a 3 m long cryostat dropped from a 40 km altitude balloon. The free-fall duration is 30 s for a non-propelled cryostat. The falling test masses are part of a high-sensitivity differential detector with a foreseeable sensitivity in detecting differential accelerations of about 1.5·10−13\(g/\sqrt {Hz} \) (at the liquid-nitrogen temperature of 77 K) and 1.5·10−14\(g/\sqrt {Hz} \) (at the liquid-helium temperature of 4 ). The detector is spun about a horizontal axis at a frequency of typically 1 Hz in order to modulate the gravity signal during free fall. The estimated accuracies, with 95% confidence level, in testing the weak-equivalence principle in a 30 s integration time are 5 parts in 1014 at the temperature of liquid nitrogen and 5 parts in 1015 at the temperature of liquid helium.