A headless compression screw (100,300) for compressing a first bone fragment and a second bone fragment, the headless compression screw comprising: an elongated shaft including a leading portion (120,320), a first intermediate portion (130,330), a second intermediate portion (140,340) and a trailing portion (150,350), said leading portion (120,320) having one or more threads defining a first outside diameter and a first lead; said first intermediate portion (130,330) being unthreaded; said second intermediate portion (140,340) having one or more threads defining a second outside diameter smaller than said first outside diameter and a second lead smaller than said first lead; said trailing portion (150,350) having one or more threads defining a third outside diameter greater than said first outside diameter and a third lead smaller than or equal to said second lead; such that, when said headless compression screw is torqueably inserted through a first bone or bone fragment and a second bone or bone fragment separated by a gap, said second bone or bone fragment is translated longitudinally towards said first bone or bone fragment; when said bone fragments are adjoining each other, further torqueing of said screw, prior to engagement by said trailing portion of said first bone or bone fragment, will maintain said second bone or bone fragment in contact with said first bone or bone fragment without causing substantial compression to occur between said first bone or bone fragment and said second bone or bone fragment, and, when further torque is applied to said screw upon engagement by said trailing portion of said first bone or bone fragment, compression will occur between said second bone or bone fragment and said first bone or bone fragment, characterised in that said headless compression screw is a one-piece screw. an elongated shaft including a leading portion (120,320), a first intermediate portion (130,330), a second intermediate portion (140,340) and a trailing portion (150,350), said leading portion (120,320) having one or more threads defining a first outside diameter and a first lead; said first intermediate portion (130,330) being unthreaded; said second intermediate portion (140,340) having one or more threads defining a second outside diameter smaller than said first outside diameter and a second lead smaller than said first lead; said trailing portion (150,350) having one or more threads defining a third outside diameter greater than said first outside diameter and a third lead smaller than or equal to said second lead; such that, when said headless compression screw is torqueably inserted through a first bone or bone fragment and a second bone or bone fragment separated by a gap, said second bone or bone fragment is translated longitudinally towards said first bone or bone fragment; when said bone fragments are adjoining each other, further torqueing of said screw, prior to engagement by said trailing portion of said first bone or bone fragment, will maintain said second bone or bone fragment in contact with said first bone or bone fragment without causing substantial compression to occur between said first bone or bone fragment and said second bone or bone fragment, and, when further torque is applied to said screw upon engagement by said trailing portion of said first bone or bone fragment, compression will occur between said second bone or bone fragment and said first bone or bone fragment, characterised in that said headless compression screw is a one-piece screw.