In this letter, we present and analyze theoretically some ideas for thin one-dimensional (1-D) cavity resonators in which a combination of a conventional dielectric material and a metamaterial possessing negative permittivity and permeability has been inserted. In this analysis, it is shown that a slab of metamaterial with negative permittivity and permeability can act as a phase compensator/conjugator and, thus, by combining such a slab with another slab made of a conventional dielectric material one can, in principle, have a 1-D cavity resonator whose dispersion relation may not depend on the sum of thicknesses of the interior materials filling this cavity, but instead it depends on the ratio of these thicknesses. In other words, one can, in principle, conceptualize a 1-D cavity resonator with the total thickness far less than the conventional λ/2. Mathematical steps and physical intuitions relevant to this problem are presented.