Drilling precise holes in concrete without bit wandering
Start with a small bit. (or maybe a diamond dremel bit.)
You still want to use a punch, then use a 1/8&quot;th bit, or smaller if you can find one. Then step up to the size you need for your anchor or screw. The small hole will help guide the larger bit.
Alternatively you could make a jig;
Drill a hole of the size you need to guide your masonry bit in a piece of wood and then use some double sided tape to stick it to the wall. The hole in the wood keeps the bit from wandering.
&quot;Not all those who wander are lost&quot;
If, after drilling, they do not line up you could plug the hole with a wood dowel and adhesive and drill that out.