Grid computing promises to bring the resources to satisfy the increasing requirements of scientific applications. As grids result from several organizations that pool their computational resources, resource availability varies frequently inside grids. Relying on autonomous dynamic adaptability and managing dynamic collections of resources, technologies have been proposed in order to handle those variations at the level of applications. However, despite applications have evolved in order to fit better dynamic grid environments, grid resource managers still restrict to rigid jobs, thus inhibiting application adaptability and malleability. This paper discusses 3 options to overcome that restriction. Malleable job management can be built on top of existing unmodified infrastructures. It can also be implemented as a modification of the infrastructure. At last, we propose an intermediate approach that fosters the cooperation between the infrastructure and its users. Requiring an initial modification of the infrastructure, the latter design combines cost efficiency with possibility to further extend the job model without any additional modification of the infrastructure. In the discussion, qualitative arguments arc supported by some experimental results.