1ES 1927+654 is an active galactic nucleus (AGN) that appears to defy the unification model. It exhibits a type-2 optical spectrum, but possesses little X-ray obscuration. XMM–Newton and Suzaku observations obtained in 2011 are used to study the X-ray properties of 1ES 1927+654. The spectral energy distribution derived from simultaneous optical-to-X-ray data obtained with XMM–Newton shows that the AGN has a typical Eddington ratio (L/LEdd = 0.014 – 0.11). The X-ray spectrum and rapid variability are consistent with originating from a corona surrounding a standard accretion disc. Partial covering models can describe the X-ray data; however, the narrow Fe Kα emission line predicted from standard photoelectric absorption is not detected. Ionized partial covering also favours a high-velocity outflow (v ≈ 0.3c), which requires the kinetic luminosity of the wind to be ≳ 30 per cent of the bolometric luminosity of the AGN. Such values are not unusual, but for 1ES 1927+654 it requires that the wind is launched very close to the black hole (∼10 rg). Blurred reflection models also work well at describing the spectral and timing properties of 1ES 1927+654 if the AGN is viewed nearly edge-on, implying that an inner accretion disc must be present. The high inclination is intriguing as it suggests 1ES 1927+654 could be orientated like a Seyfert 2, in agreement with its optical classification, but viewed through a tenuous torus.