When turning rod handles, Becky has found that rather than utilizing a 3-jaw or 4-jaw chuck in the lathe headstock, use of a cup drive center or a ring friction drive is preferable.  These friction ring drives or cup drives are ideal for use with smaller diameter turning work such as found when turning rod handles.  The center tips and friction rings are identically dimensioned at the headstock (drive end), and the tail stock (live center end).  This allows for easy end for end switching of the head and tail of the handle while maintaining centerline accuracy if needed to facilitate efficient turning or sanding of difficult wood grains.  Another advantage is that since the wooden workpiece is being turned by the lathe through friction of the cup or ring edge which digs into the drive end of the workpiece, any mishaps with wood grains or knots, or, accidental gouging by turning tools, will result in the workpiece simply slipping on the headstock ring edge, rather than breaking away from the lathe and becoming a missile.  A very nice safety feature!  With a simple retightening of the tailstock center and you can proceed without issue.  Lastly, without chuck jaws to worry about, you can turn a complete handle without the need to leave wasted material at the drive end that would need to be cut or parted off. 
Becky has at times imbedded dyed crystals or silver ribbon within her handle surface.  These cup or ring drives allows for safely making final turning cuts without issue due to the differences in surface hardness.
There may be a number of companies that produce these lathe cup or ring drives in #2Mt or #1MT tapers.  Becky is familiar and utilizes such tooling from two sources she is familiar with.  One supplier is Axminster Tools, a UK tooling company which you can buy direct from their website in England, or from one of several US distributors.  The Axeminster Ring Friction Drives as the call them comes with a threaded body.  This facilitates the use of a larger ring drive which can be purchased and threaded on in case you want to use this same ring drive for larger turning work such as a bowl.  Not something Becky utilizes in her handle turning but it is a nice feature provided by Axminster.
The other supplier is Oneway Manufacturing, a Canadian company with sales supported through numerous US distributors.  They have a spring loaded center which you can adjust the tension.  Otherwise it is nearly identical to the Axminster brand though the two companies' ring diameters are not exactly identical in size.  Becky recommends using the same brand in the headstock and tailstock to accommodate the ability to switch the workpiece end for end while maintaining centerline integrity.

​Another question Becky always seems to be asked is, "how do you accurately drill your handle through hole maintaining it on the centerline?"  Well Becky has experimented with a number of methods.  Drilling the hole on a lathe takes a long drill bit, a long lathe bed and a steady rest to support the workpiece.  This method can lead to accurate deep hole drilling, but the introduction of a steady rest and using a long small diameter unsupported drill bit can lead to errors.  In addition, the drive end of the lathe must utilize a chuck to hold the workpiece which eliminates the ability to utilize a friction ring cup drive as described above.
Utilizing a accurate drill press also works but it has its limitations.  Most drill presses do not have long travel which requires drilling 3 or 4 inches and then repositioning the table progressively closer to the chuck.  Once again, Becky has found that each time you reset-up the workpiece you are introducing a chance for error.  Drilling on a drill press usually means drilling half way through the handle and then drilling from the other end to finally have your holes meet in the center (hopefully!).
Professionals utilize specialized gun drill equipment to drill long or deep holes, but most of our budgets and shop space don't allow for that luxury.
Becky has found that the Axminster Company manufactures a Hollow Live Centre tool with Chip Ejection ports for the very purpose of through hole drilling without changing setups once a handle is turned.  This live center is utilized in conjunction with the Ring Friction Drive as described above at the headstock end of the lathe.  The hollow live center has a magnetic center plug for purposes of turning a handle between centers.  Once turned, the magnetic center plug is removed and the workpiece remounted on the drive ring indentations.  now a 5/16" lamp drill bit can be inserted in the back of the tailstock (5/16" or 8mm hole) and through the Axminster hollow live center to drill the center hole of the handle.  Working the drill in and out to clear the chips out of the live center chip ejection holes works fairly efficiently.  Axminster also sells a boring bit handle which easily grips (or releases) the lamp drill shaft for pushing the drill into the workpiece.  Becky recommends drilling about two thirds of the way through the workpiece, then removing the workpiece, turning it end for end, and remounting in the workpiece ring grooves.  Axminster also has a four prong driver head with a 5/16" locating pin that can fit into the freshly drilled end for even better centerline alignment.  Once remounted, drilling with the 5/16" lamp drill through the tailstock can complete the process of drilling the through hole.  Support provided by the tailstock and the hollow live center tool of the drill shaft through the deep hole drilling process seems to keep hole drilling straight.   Becky finds that the accuracy provided by this method is far superior than other techniques she has tried.  Progressive drilling of larger holes in the workpiece can be easily completed by hand or with the drill press.  With the accurate initial 5/16" hole on centerline, enlarging holes are drill without issue.
Though we are describing a system by Axminster which Becky utilizes and is very efficient at accurate deep hole drilling, we understand many people will not find it cost effective to invest in this tooling.  The next section below on progressive reamers may offer an alternative.