First, a 'rule-of-thumb' about perceived loudness:

3 dB is widely accepted as the minimum perceptible change in sound pressure level.

In practical terms, this means that reducing an amp's power by half (-3 dB) would produce a barely perceptible drop in volume. This is why the old trick of pulling two of the power tubes out of a four tube amp doesn't really help much, and it can cause component failure problems. And cutting a 100 Watt amp back to 50 Watts doesn't buy you much reduction in volume. Deep in the archives of the GT website are many long discussions on this subject. If memory serves, I think we arrived at the conclusion that a truly apartment-friendly power amp would be running at much less than 1 Watt!

A common approach is to connect an attenuator, sometimes called a power brake or power soak, between the amp and the speaker cab. These devices can be effective in reducing the sound level, but players often crank the amp to get lots of crunch at these lower volumes. This means the amp is running hard, and the tubes wear out quickly. A consideration is the reduced interraction between the amp and speaker. Tone is often 'not quite right' as a result.

A technique that I find interesting is called Power Scaling. In essence, this method reduces the voltages applied to the power tubes, reducing their output power. If done right, the low-level tone is consistent, and the tubes last much longer, because they aren't subjected to such high power dissipation. There are a lot of websites devoted to this stuff. Look around. Applying this technique to your deluxe would definitely involve extensive (and expensive) modifications.

If you want to leave your amp stock, I think an attenuator is probably the best way to go. Just bear in mind that if you crank the amp and drive it hard, it will be just as hard on the tubes as if you were running straight into the speakers at high volume.