SummaryVirtualized cloud infrastructures (also known as IaaS platforms) generally rely on a server consolidation system to pack virtual machines (VMs) on as few servers as possible. However, an important limitation of consolidation is not addressed by such systems. Because the managed VMs may be of various sizes (small, medium, large, etc.), VM packing may be obstructed when VMs do not fit available spaces. This phenomenon leaves servers with a set of unused resources (‘holes’). It is similar to memory fragmentation, a well‐known problem in operating system domain. In this paper, we propose a solution which consists in resizing VMs so that they can fit with holes. This operation leads to the management of what we call elastic VMs and requires cooperation between the application level and the IaaS level, because it impacts management at both levels. To this end, we propose a new resource negotiation and allocation model in the IaaS, calledHRNM. We demonstrate HRNM's applicability through the implementation of a prototype compatible with two main IaaS managers (OpenStack and OpenNebula). By performing thorough experiments with SPECvirt_sc2010 (a reference benchmark for server consolidation), we show that the impact of HRNM on customer's application is negligible. Finally, using Google data center traces, we show an improvement of about 62.5% for the traditional consolidation engines. Copyright © 2017 John Wiley & Sons, Ltd.