In this article the ability to record, store, and read out the quantum properties of light is studied. The discussion is based on high-speed and adiabatic models of quantum memory in λ configuration and in the limit of strong resonance. We show that in this case the equality between efficiency and squeezing ratio, predicted by the simple beam-splitter model, is broken. The requirement of the maximum squeezing in the output pulse should not be accompanied by the requirement of maximum efficiency of memory, as in the beam-splitter model. We have demonstrated that for the same optical depth a high output pulse squeezing can be reached earlier than the high efficiency. Comprehension of this "paradox" is achieved on the basis of mode analysis. The memories eigenmodes, which have an impact on the memory process, are found numerically. Also, the spectral analysis of modes was performed to match the spectral width of the input signal to the capacities of the memories.