Approximations for the linear elastic properties of non-dilute solid suspensions made of parallel circular fibers with imperfect interfacial bonding are proposed. Elastic anisotropy of the reinforcements and the matrix can be arbitrary, but that of the interfacial bond is restricted to a particular form of common use. Three distinct estimates which display the same mathematical structure but differ in the way the interfacial compliance is averaged over the interface are compared. Based on the use of alternative equivalent stiffness tensors for the reinforcing phase, they either involve an ‘arithmetic’, a ‘harmonic’ or a ‘mixed’ mean of the bonding compliance. The estimates are applied to isotropic suspensions and confronted to full-field computations for assessment. Numerical results are carried out by means of a Fast Fourier Transform (FFT) algorithm suitably implemented to handle solid suspensions with imperfect interfaces on the basis of more recent works by Zecevic et al. (2022) and Lebensohn et al. (2012). Aside from outperforming the ‘arithmetic’ estimate, oftenly used in mean-field descriptions based on modified Eshelby tensors, the ‘mixed’ estimate is found to be slightly more accurate than the ‘harmonic’ estimate in the reported cases.