A threaded connection (10, 10A, 10B, 10C) for connecting a pair of pipes using a coupling (5, 5A, 5B, 5C), comprising: a pair of pipes ((6,7), (6A, 7A), (6B, 7B), (6C, 7C)) and a coupling (5, 5A, 5B, 5C), the threaded connection further comprising: a pair of pins ((1, 2), (1A, 2A), (1B, 2B), (1C, 2C), (1D, 2D)), each of the pins provided on a pipe end of an associated one of the pipes ((6, 7), (6A, 7A), (6B, 7B), (6C, 7C)), including a wedge male thread having a varying-thread-width portion and a constant-thread-width portion, and including a shoulder (12, 22) on a tip of the pin; and a pair of boxes((3, 4), (3A, 4A), (3B, 4B), (3C, 4C)), each of the boxes provided on an associated end of the coupling and including a wedge female thread having a varying-thread-width portion and a constant-thread-width portion, wherein the male thread engages the female thread, the varying-thread-width portion of the pin is located adjacent to the shoulder of the pin and the constant-thread-width portion of the pin is located adjacent to a base of the pin, and the threaded connection is constructed such that, when stab flanks and load flanks in the varying-thread-width portions of the male threads of the pins of the pair of pipes contact stab flanks and load flanks, respectively, in the varying-thread-width portions of the female threads of the boxes such that a make-up torque increases from a locked-flank torque level to a shouldering torque level, the shoulders (12, 22) of the pins of the pair of pipes are not in contact with each other, and, with a further rotation in a make-up direction, the shoulders (12, 22) of the pins of the pair of pipes are capable of contacting each other before the threads yield and the make-up torque further increases above the shouldering torque level. a pair of pins ((1, 2), (1A, 2A), (1B, 2B), (1C, 2C), (1D, 2D)), each of the pins provided on a pipe end of an associated one of the pipes ((6, 7), (6A, 7A), (6B, 7B), (6C, 7C)), including a wedge male thread having a varying-thread-width portion and a constant-thread-width portion, and including a shoulder (12, 22) on a tip of the pin; and a pair of boxes((3, 4), (3A, 4A), (3B, 4B), (3C, 4C)), each of the boxes provided on an associated end of the coupling and including a wedge female thread having a varying-thread-width portion and a constant-thread-width portion, wherein the male thread engages the female thread, the varying-thread-width portion of the pin is located adjacent to the shoulder of the pin and the constant-thread-width portion of the pin is located adjacent to a base of the pin, and the threaded connection is constructed such that, when stab flanks and load flanks in the varying-thread-width portions of the male threads of the pins of the pair of pipes contact stab flanks and load flanks, respectively, in the varying-thread-width portions of the female threads of the boxes such that a make-up torque increases from a locked-flank torque level to a shouldering torque level, the shoulders (12, 22) of the pins of the pair of pipes are not in contact with each other, and, with a further rotation in a make-up direction, the shoulders (12, 22) of the pins of the pair of pipes are capable of contacting each other before the threads yield and the make-up torque further increases above the shouldering torque level.