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A piston–cylinder cell has been constructed which makes it possible to achieve pressures of over 35 kbar at room temperature, and more than 29 kbar in a cryogenic environment. The use of a nonmagnetic cobalt–nickel alloy with an unusually high yield strength (1.97 GPa at 293 K) allows the cell to be used in the presence of large magnetic fields. It seems likely that the cobalt–nickel material can be used as a direct replacement for the celebrated (but largely unavailable) Russian nickel alloy in many applications where nonmagnetic pressure cells are needed. Such applications may also include other kinds of high pressure apparatus, such as diamond anvil and sapphire anvil cells. The pressure cell described in the present article employs the “Teflon cap” technique, and detailed information concerning the application of this method is given which can be used with a wide variety of cells of the piston–cylinder type. © 1999 American Institute of Physics.