The paper introduces a concept of a "negotiated space" to describe university researchers' attempts to balance pragmatically, continually and dynamically over time, their own agency and autonomy in the selection of research topics and pursuit of scientific research to filter out the explicit steering and tacit signals of external research funding agencies and university strategies and policies. We develop this concept to explore the degree of autonomy researchers in fact have in this process and draw on semi-structured interview material with research group leaders in Finland and the UK, in the former in seven research fields, in the latter in two fields. First, the analysis reveals that topic selection is strongly filtered by the intra-scientific factors. In topic selection researchers have more leeway, a broader negotiated space than in research content, that is, in the ways in which they pursue their research, which are more affected by funding opportunities and other contextual matters. Second, the ways which affect researchers' agency include individual- and more aggregate-level acts and factors: at the individual level, researchers resort to different strategies to create a negotiated space, but at the more aggregate level field-specific factors play a role. In fields with multiple funding opportunities, which we call "shopping mall" fields, researchers can have a broader negotiated space than in fields where funding is more based on "lottery". In the latter, the researchers' negotiated space is narrow and contingent on the outcome of the funders' decisions.