In map-predictive exploration planning, the aim is to exploit a-priori map information to improve planning for exploration in otherwise unknown environments. The use of map predictions in exploration planning leads to exacerbated greediness, as map predictions allow the planner to defer exploring parts of the environment that have low value, e.g., unfinished corners. This behavior is undesirable, as it leaves holes in the explored space by design. To this end, we propose a scoring function based on inverse covisibility that rewards visiting these low-value parts, resulting in a more cohesive exploration process, and preventing excessive greediness in a map-predictive setting. We examine the behavior of a non-greedy map-predictive planner in a bare-bones simulator, and answer two principal questions: a) how far beyond explored space should a map predictor predict to aid exploration, i.e., is more better; and b) does shortest-path search as the basis for planning, a popular choice, cause greediness. Finally, we show that by thresholding covisibility, the user can trade-off greediness for improved early exploration performance.