With the objective of understanding the role of size and current level of filamentary regions on the resistive switching parameters, detailed conductive atomic force microscope investigations of resistive memory cells having different dimensions have been carried out in this study. Cu-Cu(2)O-Ti memory cells having dimensions of 150, 50 and 25 μm have been fabricated on the same substrate using a stencil lithography technique. The dependence of resistive switching parameters on the device dimensions can be directly related to the average size, current level of the filaments and difference in these parameters between the low resistance state (LRS) and high resistance state (HRS). It is observed that the large increase in the ratio of current in the two states in cells having lower dimensions is mainly due to the smaller number of conducting regions in the HRS, indicating efficient switching from the LRS to the HRS at lower dimensions.