If you just want to try something different DD-X is a great choice in place of Xtol, I moved to DD-X for the same reason. It's easy to use, reliable, and like Xtol helps salvage a little extra shadow detail when a film is underexposed.
Some thoughts to consider though.
First, since you didn't meter, how do you know?
I'm not suggesting you have to meter, there are other clues to use. I'm just asking if this is a guess or based on something else.
Neither reducing nor adding extra exposure automatically means that a push or pull is needed or preferable. All it means is that you have placed your subject matter differently on the film, closer or farther from the toe. What pushing and pulling actually do is change the steepness of the film curve and it's relationship to the paper, these techniques don't change the film's measured speed much.
Developers like Xtol and DD-X will give slightly faster measured film speeds than say D-76 or ID-11 (roughly 1/3-stop, so 500 instead of 400) but Xtol and DD-X do not differ significantly from each other with regard to film speed (500 vs 500).
Pushing and pulling also do not change this basic speed point (500 in this case) much. A 2-stop push, using Xtol or DD-X or similar, might get you into the 800-1000 range, if your real lucky and depending on how you measure speed, thinking you are going to get more than that is pretty much just wishful thinking. The point here is that as-a-rule as you reduce exposure you truly do lose shadow detail, that's simply the physics of it.
Testing for yourself; your film, your developer, your subjects, your shooting style, your metering style (or lack thereof

)... is how you figure out where your limits are. For me about 1-stop under box speed is typically quite workable but that uses up all of my safety factor, any more than that and it can start cutting into the shadow detail I wanted to print. Kodak starts recommending pushing Tri-X at 1600, at 800 process as you would for 400. Shooting at 800 and processing at 400 is an example of using up this safety factor.
Keeping my film processing "normal" (say as specified for 400) maintains the subject matter's "look" in the print and that is the crux of the issue for me. Even if I am forced to under or over expose to get a shot, I normally don't want the look of the subject matter to change. Pushing and pulling change the look of the subject.