Many insignificant events in our daily life are forgotten quickly but can be remembered for longer when other memory-modulating events occur before or after them. This phenomenon has been investigated in animal models in a protocol in which weak memories persist longer if exploration in a novel context is introduced around the time of memory encoding. This study aims to understand whether other types of rewarding or novel tasks, such as rewarded learning in a T-maze and novel object recognition, can also be effective memory-modulating events. Rats were trained in a delayed matching-to-place task to encode and retrieve food locations in an event arena. Weak encoding with only one food pellet at the sample location induced memory encoding but forgetting over 24 h. When this same weak encoding was followed by a rewarded task in a T-maze, the memory persisted for 24 h. Moreover, the same persistence of memory over 24 h could be achieved by exploration in a novel box or by a rewarded T-maze task after a "non-rewarded" weak encoding. When the one-pellet weak encoding was followed by novel object exploration, the memory did not persist at 24 h. Together, the results confirm that place encoding is possible without explicit reward, and that rewarded learning in a separate task lacking novelty can be an effective memory-modulating event. The behavioral and neurobiological implications are discussed.