>>>>Stating the obvious here, but could the lamp itself be faulty?
>>>
>>>LampS. They both act exactly the same way.
>>
>>Is your 3-way bulb bad?
>>
>>~~Bonnie
>
>Brand new, but possibly I guess.

She may be onto something. I have seen that behavior when one of the filaments goes out -- the 3 way bulb starts acting like a 1 way bulb, with two blank switch states. Can you try another 3 way bulb?