Disclosed is a process for making bulky nonwoven fabric suitable for use in diaper constructions that comprises the steps of (a) forming a web of one or more layers comprised at least in part of thermoplastic bicomponent fibers, (b) bonding said web by means of a thru-air system, (c) compressing--either in a nip or by winding--the resulting bonded web to increase its density, (d) transporting and/or otherwise manipulating the compressed web, and (e) subsequently transforming said compressed web, by means of exposure to heat, into the low density bulky nonwoven fabric. The bulky nonwoven fabrics are particularly useful as diaper coverstock and as diaper spacer fabrics.