All lancets are not the same. Most people use the lancet that came with their meter. If you research lancets you will find several differences. The one you are now using may not be your best choice. I know this because the one that came with my meter wasn't the best one for me.  
I managed to drop part of the lancet down my bathroom drain more than once. I would stick myself when I reached into the lancet container because the lancet's cover had come off and I didn't notice it had no cover – ouch! I would stick myself with the used lancet when I tried to put the tip back in the round cover – another owie!

Many meter companies say you need less blood to use their meter/test strips than was needed in the past. In my experience the statement is a partial truth. I have not been able to squeeze my finger precisely enough to have the minimum amount of blood bead up every time. If I have too little blood my meter gives me an error message and I've wasted a test strip – frustrating. I realized the amount of blood squeezed out of my finger tip is not something to be concerned about. Under no circumstances will I have several drops of blood to deal with.  

Lancets come in a few different styles. Most lancet makers say their lancets will fit in most lancing devices. My experience confirms their statements.

Did you know the larger the number of the lancet the thinner the lancet? A 26 gauge lancet is larger than a 33 gauge lancet. If you want a smaller hole in your finger tip you need a thinner lancet. A smaller hole will heal quicker that a larger hole. A smaller hole will hurt less and stop bleeding sooner than a larger hole. I'm all for less pain – aren't you?

Below is an image of some lancets and their covers plus a lancing device. I've removed the covers so you can see the lancet tip. 

You need to know the skin on your finger tips is thicker or thinner depending on which finger and where on your fingers you choose to stick. One lancet maker recommends the lancet be applied to the side of your finger as the puncture wound will be less painful because you won't be pressing directly on it after the blood draw.
The lancet device I use came preset at 3 in a range of 1 to 8. One is the shallowest setting. After some experimentation I set the device at 1 only. You can get a nice drop of blood at the shallowest setting too. You can control the depth of the puncture by how hard you press you finger tip against the device. The harder you press - the deeper the puncture. Sometimes I get lucky and there is almost no pain with the right amount of blood to test.

Animals get diabetes too. They need to have their blood sugar measured with a meter/strip. Veterinarians suggest a 26 gauge lancet. The benefit of a 26 gauge lancet is that the hole will bleed without the need to be squeezed. Again, the smaller the lancet gauge you use the less of a wound with less pain.  

I have a lancet I like because it is 33gauge and has a cover that fits snuggly so I don't stick my self accidentally and the shape of the cover is less likely to roll into my sink and down the drain.