1. A downhole steering tool configured to operate in a borehole, the steering tool comprising: a shaft deployed substantially coaxially in a housing, the shaft and the housing being free to rotate relative to one another about a longitudinal axis of the steering tool; a plurality of blades deployed on the housing, the blades disposed to extend radially outward from the housing and engage a wall of the borehole, said engagement of the blades with the borehole wall operative to eccenter the housing in the borehole; a plurality of circumferentially spaced formation evaluation sensors deployed in the housing, each of the formation evaluation sensors being configured to individually provide a corresponding azimuthally focused sensor response, the plurality of formation evaluation sensors being configured to collectively provide a non-azimuthally focused sensor response; and a controller configured to acquire sensor data from the formation evaluation sensors and to compute both azimuthally focused and non-azimuthally focused formation evaluation measurements.