A set of containers, preferably graduated and conveniently ranging in size generally from 1/2 pint to 1 gallon, each having a lid that may be placed on top to seal its respective, container and also may be matingly attached to the bottom in order that a smaller container with lid attached may be nested in the next larger container for convenient storage without loss or misplacing the lid. The lid attached to the bottom is configured to provide a uniform space between the vertical sides and the bottoms of nested containers so that two nested containers may provide a double walled container with an air gap acting as thermal insulation. Each lid may have a rim with a scalloped outside surface to prevent trapping of air in the nested position that could otherwise impede removal of the container and its lid from a larger container. A flange or downturned lip may be provided adjacent the upper rim of the container to assist in supporting a smaller inner container or a larger in a spaced relationship. A preferred embodiment employs a button (or knob) in the lid to engage an appropriately shaped and sized recess in the bottom of the container or vice versa.