@russellcsloan I created a new thread for this since you are reporting a separate issue.
While there isn't currently a way to easily block specific artists from playing in Deep Cuts Mode, I recommend creating a feature request if that is something you'd like to see added to the service. You can create a feature request here.
In the meantime, continue to use the Thumbs Up/Down options on your stations.
Pandora stations adapt with every song to try to find the right music for your stations. Without Thumb info, however, Pandora has to guess what songs you like or don't like, which can often lead to the problem you've described. Keep in mind, Thumbs are station specific, so please feel free to Thumb up and down accordingly. Giving a Thumb rating on one station will not affect any of your other stations. This also means that you can use Thumbs to craft the sound you are trying to achieve and vary the playlists from station to station. For example, you might want to give a song you like a Thumb Down if you think it will bring in a certain type of music you'd prefer to not have on that station. Don't be afraid to rate songs (you can always edit your stations later if you don't like the direction your station is going or if you'd like to mix things up).
Let me know if this helps!
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