Is there a possiblity you could post here your step-by-step instructions on how you make those joints?
For you Neb, I am happy to: Keep in mind the finished product above and refer to the pictures below.
I had a stick that needed a handle and a "T" handle was the most obvious choice. I started with a scrap block of wood 1-1/2" thick (the remainder seen in the pictures below) and drew the basic shape I wanted for the finished handle on the block. This showed me where I needed to bore my hole which I then bored using the bit in the picture. The bit I used was made by Stanley and is called a "powerbore" bit. Sadly, Stanley no longer makes these - they bore a very clean, smooth, accurate hole, but any similar bit will do. I bored through the block until the tip of the spur just barely poked through the other side, then turned the block over, placed the tip of the spur in the small hole it made and finished boring from the opposite side to prevent tearout and get a nice clean hole. Once the 3/4" bore was finished, I then shaped my handle. I did it in this order because it was easier to bore my hole in a rectangular block than the finished handle and I eliminated the chance of tearout by shaping with the hole already in place
Next, I traced a 3/4" circle on top of the shaft to use as a guide to whittle my tenon. I did numerous sizing checks along the way to assure a nice round tenon and a snug fit. I made the length of the tenon so that it protruded about 1/4" above the handle. Once I had the shaft and handle mated satisfactorily, I marked the bottom of the handle on the shaft to show me how deep to cut the notch for my wedge.
I cut the notch for the wedge with a hack saw (any fine-toothed saw will do. I do have some special dovetail saws I could have used, the hacksaw was close at hand). See below for pictures of the wedge and notch (quickly cut in a piece of scrap for the sake of the picture- the one I cut for my cane was more precise). The purpose of the wedge is to spread the top of the shaft to lock it in the hole. It expands the top of the shaft, forcing it out against the hole sides providing a nice tight fit.
Once everything was fit, I buttered it the inside of the hole with glue and a small brush and rubbed glue on the tenon and on insides of the saw kerf for the wedge and put it all together. Then I rubbed glue on the wedge and drove it in with a hammer. You don't want the wedge too big - it might split the wood if too much pressure is applied, but it has to be tight enough to do its job. I then cleaned off the excess glue with a damp rag which immediately raised all the grain on the handle and shaft near the handle. Once the glue had set long enough to, I trimmed the portion of the shaft protruding above the handle, resanded everything and applied finish.
This technique can be used with a segment of tree limb for a handle too, you just need to figure out how to hold it to bore it safely and cleanly. If this wasn't clear enough, please feel free to ask any questions you may have.