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We study harmonic sections of a Riemannian vector bundle E → M whose total space is equipped with a 2-parameter family of metrics h p,q which includes both the Sasaki and Cheeger-Gromoll metrics. The restrictions of the h p,q to the total space of any sphere subbundle SE(k) of E (where k > 0 is the radius) are essentially the same for all (p, q), and it is shown that for every k there exists a unique p such that the harmonic sections of SE(k) are harmonic sections of E with respect to h p,q for all q. In both the compact and non-compact cases Bernstein regions of the (p, q)-plane are identified, where the only harmonic sections of E with respect to h p,q are parallel. Examples are constructed of compact vector fields which are harmonic sections of E = T M in the case where M has non-zero Euler characteristic.1991 Mathematics Subject Classification. 53C43 (53C07, 53C24, 58E15, 58E20, 58G30).