Excited states in the highly neutron-deficient nucleus W-162 have been investigated via the Mo-92(Kr-78, 2 alpha) W-162 reaction. Prompt gamma rays were detected by the JUROGAM II high-purity germanium detector array and the recoiling fusion-evaporation products were separated by the recoil ion transport unit (RITU) gas-filled recoil separator and identified with the gamma recoil electron alpha tagging (GREAT) spectrometer at the focal plane of RITU. gamma rays from W-162 were identified uniquely using mother-daughter and mother-daughter-granddaughter alpha-decay correlations. The observation of a rotational-like ground-state band is interpreted within the framework of total Routhian surface (TRS) calculations, which suggest an axially symmetric ground-state shape with a gamma-soft minimum at beta(2) approximate to 0.15. Quasiparticle alignment effects are discussed based on cranked shell model calculations. New measurements of the W-162 ground-state alpha-decay energy and half-life were also performed. The observed alpha-decay energy agrees with previous measurements. The half-life of W-162 was determined to be t(1/2) = 990(30) ms. This value deviates significantly from the currently adopted value of t(1/2) = 1360(70) ms. In addition, the alpha-decay energy and half-life of Os-166 were measured and found to agree with the adopted values.