Medicare Supplements can have a six-month wait on pre-existing conditions, unless you have had at least six months of previous health coverage that can be considered "credible coverage". A pre-existing condition is a condition for which medical advice was given or treatment was recommended by or received from a physician within 6 months before the effective date of coverage. In some cases, the Medicare supplement company can refuse to cover your out-of-pocket costs for these pre-existing health problems for up to six months. If you have had less than six months of credible coverage, the six month wait on pre-existing conditions is reduced one month for each month of credible coverage.
You would definitely prefer your medicare supplement to not have a six month wait, since a health problem that was diagnosed or treated during the wait would not be covered.
What constitutes creditable coverage? Generally speaking, any other health coverage you had prior to starting on Medicare supplement policy: group health, individual health policy, medicare Part A or B, medicaid, Tricare, etc.