Animals form memory types that differ in duration and stability. The initial anaesthesia-sensitive memory (ASM) can be replaced by anaesthesia-resistant memory (ARM), and/or by protein synthesis-dependent, long-term memory (LTM). We previously showed that two closely related parasitic wasp species differ in learning rate and memory consolidation. In Cotesia glomerata, LTM lasting at least 24 h was formed after single-trial conditioning, whereas single-trial conditioning led to ARM that waned before 24 h in Cotesia rubecula. This species formed LTM only after repeated conditioning trials spaced in time. Here, we used artificial selection on learning rate to investigate whether selection for a low learning rate in C. glomerata would result in C. rubecula-like memory dynamics. Memory consolidation was tested by using cold-shock anaesthesia and protein synthesis inhibitors. After single-trial conditioning, ARM was consolidated within hours in unselected C. rubecula, but directly, without an intermediate ARM phase, into LTM in unselected C. glomerata. We obtained low learning rate selection lines of C. glomerata wasps that, like C. rubecula, did not form LTM after single-trial conditioning, to see whether such wasps would then consolidate ARM instead of LTM. We showed that this was not the case. The selected wasps formed LTM after repeated, spaced conditioning trials, but formed only ASM without consolidation of ARM or LTM after single-trial learning. Ecological consequences of this type of memory formation are discussed.