A poppet valve has a valve head and a valve stem. A piston is capable of reciprocating motion relative to a housing along a reciprocation axis. The piston has a valve-receiving portion for receiving therein an end portion of the valve stem. A cotter secures the valve stem to the piston. A cap is disposed around the valve-receiving portion. A cap lateral portion extends away from the cap end portion in the direction of the valve head. The valve-receiving portion is held between the cap end portion and the cap lateral portion in a direction parallel to the reciprocation axis. At least part of the cap lateral portion is angled toward the reciprocation axis. The part of the cap lateral portion is closer to the reciprocation axis than at least part of the valve-receiving portion. A method of assembling a valve assembly is also described.