The current document is directed to length-adjustable catheters and methods that employ length-adjustable catheters to treat malformations, constrictions, obstructions, lesions, and blockages within patients' blood vessels. The length of the shaft of a length-adjustable catheter, to which the current application is directed, can be adjusted over a range of lengths prior to and during medical procedures. In many implementations, length adjustment is accompanied by indications, to the medical provider, of the extent of a length adjustment. The indications may include one or more of visual markings, haptic feedback, radio-opaque markings, and/or other types of indications. In many implementations, the variable-length mechanism of the length-adjustable catheter is mechanically lockable following length adjustment.