Pocketable .380's are numerous. This link to a sticky in this forum gives pictures and dimensions:
http://www.thehighroad.org/showthread.php?t=171820
Most small pocket .380's are in the 11 oz class unloaded. It takes polymer to get them that light, so it becomes a required item. Alloy frame guns are generally heavier and higher priced which don't make them worse but put them at a disadvantage if weight and price are used as a criteria.
A decent trigger is important, and unfortunately it seems the most popular guns sold exhibit poor triggers and aren't the most comfortable shooters, either. To get a good trigger and a working gun pleasant to shoot costs money, and the least expensive ones on the market traded those benefits off to be the low price leader. Most pocket .380's are DA - you pull the trigger thru to fire it. Because of that they delete a separate safety but require a holster even in the pocket to cover the trigger.
You have to go out and either dry fire or rent them to discover what trigger you prefer. It can't be done second hand off an internet screen. What can be done is to pay attention to the pound weight of the trigger listed and to sort them accordingly. Not everyone prefers a 12 pound trigger, and not all of us will suffer the additional cost of a trigger upgrade to "fix" it when you could have simply purchased a better gun for the total price.
Length of trigger pull is also important. The P238 has a nice short crisp pull, the typical DA not so much. Some are quite long and where your finger rests naturally on them can also change it's feel - the higher up the shorter the trigger but heavier the pull. Hinged triggers are the norm and your natural gripping position can make one acceptable while the other a less optimal choice - even if the specs looked better on paper. Be aware some triggers requiring pulling almost all the way back to the frame to discharge - better to discover that up front before you buy.
Another significant feature is a slide hold open on last shot. The less expensive guns delete the feature but it's a false savings for two reasons: First, a gun that holds open on the last shot signals You Are Out of Ammo, vs the dreaded "click" when you needed one more round. Second, a slide hold open means you don't rack the gun every time you load a magazine, and you don't have to load that mag against the stack pressure of the springs in it under the slide. It's a frequent and even amusing thing to see a magazine fall out of the grip at the range while racking the slide on those guns, but it's not funny when it's important, and it's less safe to have to rack it every time just to enjoy shooting a box of ammo.
If you can't enjoy shooting a box of ammo with it at the range, you won't, and it becomes an unknown gun when you really need it. "I probably won't ever shoot it in self defense" doesn't really cut it as an excuse. And why buy a gun that is less than comfortable or has snappy recoil known to strike your shooting knuckles?
Try a Kahr CW380 and see if the trigger falls inside your expectations. For many it's much smoother and shorter than a lot of other pocket guns. The recoil spring is stiffer but it shoots more easily and with the slide hold open you aren't racking it every magazine like it or not. It's also a much more pleasant gun to shoot at the range which increases your familiarity with it and you make less mistakes using it because of more proficiency. The trigger pull is DA but it's at the 6 pound end of the scale, not 12 like others recommended. It was done right the first time by a company who's triggers have always excelled, not like some others which immediately got aftermarket triggers to improve what was apparently a poor one to begin with. The gun weighs in the 11 oz class, it's polymer so it's under $350, in the typical price range of the better guns - unlike the cheaper stripped featureless ones in their third generation attempting to get the trigger right. It has magazines available at dealers and Mag Guts also makes +1 spring and follower kits to add capacity if that's desired, with good results across the board. That makes it a 8 shot pistol with one up, something not always available with others. Good sights are on it from the factory and night sights are available.
I owned a first Gen LCP and the newer ones have reportedly better triggers but it doesn't make them better shooters at the range. They are snappy and two magazines were the limit. The Kahr got a box of 50 the first day and even loading the one magazine was a pleasant experience with controlled recoil and good accuracy. I can say you can definitely buy worse triggers than a Kahr in this category and constantly racking the slide on some of them - like the LCP - can definitely take some of the joy out of a range trip.
Go shoot them if at all possible - It has to fit your hand and your expectations. It may even result in choosing something different, but if it works, good. If not, then it's another waste of time and money that was preventable and it only fills up another listing in a gun for sale forum as something that didn't work. We can all get used to any gun regardless, but for some certain features and time work against us and it's better to spend some of it up front sorting them out rather than later tossing them out.