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Spiking neural networks (SNNs) are good candidates to produce ultra-energy-efficient hardware. However, the performance of these models is currently behind traditional methods. Introducing multi-layered SNNs is a promising way to reduce this gap. We propose in this paper a new threshold adaptation system which uses a timestamp objective at which neurons should fire. We show that our method leads to state-of-the-art classification rates on the MNIST dataset (98.60%) and the Faces/Motorbikes dataset (99.46%) with an unsupervised SNN followed by a linear SVM. We also investigate the sparsity level of the network by testing different inhibition policies and STDP rules.