Spike-frequency adaptation is known to enhance the transmission of information in sensory spiking neurons, by rescaling the dynamic range for input processing, matching it to the temporal statistics of the sensory stimulus. Achieving maximal information transmission has also been recently postulated as a role for Spike-Timing Dependent Plasticity (STDP). However, the link between optimal plasticity and STDP in cortex remains loose, and so does the relationship between STDP and adaptation processes. We investigate how STDP, as described by recent minimal models derived from experimental data, influences the quality of information transmission in an adapting neuron. We show that a phenomenological model based on triplets of spikes yields almost the same information rate as an optimal model specially designed to this end. In contrast, the standard pair-based model of STDP does not improve information transmission as much. This result holds not only for additive STDP with hard weight bounds, known to produce bimodal distributions of synaptic weights, but also for weight-dependent STDP in the context of unimodal but skewed weight distributions. We analyze the similarities between the triplet model and the optimal learning rule, and find that the triplet effect is an important feature of the optimal model when the neuron is adaptive. If STDP is optimized for information transmission, it must take into account the dynamical properties of the postsynaptic cell, which might explain the target-cell specificity of STDP. In particular, it accounts for the differences found in vitro between STDP at excitatory synapses onto principal cells and those onto fast-spiking interneurons.