This is more common than most think, but is easily addressed by a properly measured, custom shirt. Custom shirts are made to your specific measurements. Each arm is individually measured, along with each wrist, your neck, chest, etc.
If you are purchasing a shirt off-the-rack, and know your sleeve lengths, always purchase a shirt whose sleeve length is at least as long as your longer arm. If the shirt has buttons, you can have your tailor tighten the wrist of the shorter arm by moving the button on the cuff of the shorter arm, so that the shirt stops at the break in your wrist. While there will technically be a little excess fabric in the arm of the shorter sleeve, your sleeves will appear to be the same length.
If you are purchasing a shirt with cuff links, your only alternative to a custom shirt is to have a tailor shorten one of your sleeves. They do this by removing the cuff, cutting the sleeve to your length, and re-applying the cuff.
The alternative to the above options, is of course, to be fitted for a custom shirt. Your sleeves will be perfect.
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