The learning ability of lightweight CNN-based models is usually modest due to lack of spatial diversity in feature extraction as well as the imperfection of aggregated spatial information for identity mappings. To deal with these problems, we introduce an efficient lightweight model by addressing three novel concepts as follows. i) A novel perceptive block is proposed to extract discriminative moment-residual-coherent features (named MRCF) from depthwise-based tensors. ii) To adapt to the channel-elasticity moments of MRCF in a shallow backbone, two novel adaptive residual mechanisms are presented: an increase-moment residual is based on the expanding flexibility of a pointwise operator, while the decrease-moment one is on the aggregated spatial patterns of a fused tensor. To the best of our knowledge, it is the first time that an identity-mapping mechanism is structured for condensed-spatial information without increasing the model complexity. iii) A lightweight network is introduced by addressing three robust caret-shape segments of MRCFs. Experiments on various benchmark datasets have verified the efficacy of our proposals. All codes are available at https://github.com/nttbdrk25/CaretNet