A dilator-sheath combination comprising: an elongate tubular sheath, wherein the elongate tubular sheath comprises a sheath body, a sheath proximal end, and a sheath distal end, wherein a thickness of the sheath distal end is less than a thickness of the sheath body, wherein an outer diameter of the sheath distal end has a portion tapering in a direction from the sheath proximal end toward the sheath distal end, wherein the sheath body has a lumenal radius and the sheath distal end has an inner radius, and wherein the sheath proximal end comprises a sheath housing defining an aperture; and a dilator comprising an elongate dilator shaft including a dilator proximal end and a dilator distal tip, wherein the dilator has a dilator hub at its proximal end, wherein the dilator distal tip comprises a dilator bump being a radially enlarged dilation member, wherein the dilator bump comprises a proximal taper that increases in radius from the proximal to distal direction, wherein the dilator bump comprises a distal taper that decreases in radius from the proximal to distal direction, wherein the dilator bump has a maximal radius (86, 96), at a point between the proximal taper and the distal taper, the maximal radius of the dilator bump being greater than the inner radius of the sheath distal end, and wherein the dilator bump is capable of being passed through the sheath body by radially stretching the sheath distal end wherein, when the dilator and the sheath are in an assembled state, the assembled dilator-sheath combination comprises a gap as measured longitudinally between a distal gap terminus and a proximal gap terminus, wherein said gap has a gap length (28, 61), wherein said distal gap terminus is defined as a point of minimal radius of the proximal taper of the dilator bump, and wherein said proximal gap terminus is defined as a distal point of the sheath distal end. an elongate tubular sheath, wherein the elongate tubular sheath comprises a sheath body, a sheath proximal end, and a sheath distal end, wherein a thickness of the sheath distal end is less than a thickness of the sheath body, wherein an outer diameter of the sheath distal end has a portion tapering in a direction from the sheath proximal end toward the sheath distal end, wherein the sheath body has a lumenal radius and the sheath distal end has an inner radius, and wherein the sheath proximal end comprises a sheath housing defining an aperture; and wherein the dilator has a dilator hub at its proximal end, wherein the dilator distal tip comprises a dilator bump being a radially enlarged dilation member, wherein the dilator bump comprises a proximal taper that increases in radius from the proximal to distal direction, wherein the dilator bump comprises a distal taper that decreases in radius from the proximal to distal direction, wherein the dilator bump has a maximal radius (86, 96), at a point between the proximal taper and the distal taper, the maximal radius of the dilator bump being greater than the inner radius of the sheath distal end, and wherein the dilator bump is capable of being passed through the sheath body by radially stretching the sheath distal end wherein, when the dilator and the sheath are in an assembled state, the assembled dilator-sheath combination comprises a gap as measured longitudinally between a distal gap terminus and a proximal gap terminus, wherein said gap has a gap length (28, 61), wherein said distal gap terminus is defined as a point of minimal radius of the proximal taper of the dilator bump, and wherein said proximal gap terminus is defined as a distal point of the sheath distal end.