Mix together the salt, pepper, paprika, garlic, cayenne pepper, ground mustard, and brown sugar.
Trim the excess fat off the pork and pat the pork dry. Brush the olive oil on all sides and sprinkle the dry rub along the meat. Use your fingers to gently press and rub the spice mixture along the meat.
Preheat the smoker to 225 degrees.
Move the pork into the smoker, close the lid, and smoke until it reaches 145 degrees. This can take between 1.5-3 hours.
Place the pork on a clean plate to rest for 10-15 minutes before slicing and serving.
Notes
If desired, wrap the pork tenderloin in foil once it reaches about 120 degrees. Then, continue the cooking process until it reaches 145 degrees. This helps the pork remain moist during the last stretch of the smoking process.