Hi Linda, thank you for the detailed review. The pepper version has a different adjustable grinding mechanism than the matching salt mill, and some movement between the upper and lower portions can be normal as the mill is turned during use. The pepper mill also has four selectable grind settings, while the salt mill uses a different mechanism.
That said, it should not feel excessively loose or unstable. Since both of the pepper mills you received feel the same way, it may simply be normal play in the design, but if either one seems unusually loose or isn't grinding properly, please contact us and we'll be happy to help.
