A method of making a tackified nonwoven sheet that includes forming a densified, tackified web by providing a rebulkable nonwoven fiber web and applying an adhesive to the nonwoven web. The densified, tackified web is rebulked to an open, lofty form by exposing the densified, tackified web to a temperature of at least 225° F. Finally, a sheet is formed from the rebulked, tackified web. In some embodiments, the so-formed sheet is a cleaning wipe configured for picking up diverse debris such as sand, dust, hair, and/or food particles. In other embodiments, the method further includes the rebulked, tackified web having an increased degree of loftiness as compared to a degree of loftiness of the densified, tackified web prior to rebulking.