A system for performing kidney replacement treatment or for performing kidney replacement treatment with enhanced convective clearance and reduced blood clotting risk, comprising: a hemodialysis system having: (i) a controlled compliance dialysis circuit having a substantially inflexible volume; (ii) an extracorporeal circuit having a conduit for receiving blood from a subject and a conduit for returning blood to the subject, and a blood pump for conveying blood from the subject, to the dialyzer and back to the subject; and (iii) a dialyzer with a dialysis membrane wherein blood and a dialysate contact different sides of the dialysis membrane, a blood inlet end for receiving blood, a blood outlet end for allowing blood out of the dialyzer, a dialysate inlet end for receiving dialysate and a dialysate outlet end for allowing dialysate out of the dialyzer; wherein the controlled compliance dialysis circuit comprises: (iv) a dialysis circuit having a sorbent cartridge for removing at least one impurity or waste species from the dialysate, one or more conduits for conveying dialysate between the sorbent cartridge and the dialyzer, and a dialysate pump for conveying dialysate from the sorbent cartridge, to the dialyzer and back to the sorbent cartridge, the sorbent cartridge having a dialysate inlet end and a dialysate outlet end; (v) a control pump configured to move fluid bi-directionally between the dialysis circuit and the extracorporeal circuit, and where a flux of fluid moving between the extracorporeal circuit and the dialysis circuit is changed by the rate at which the control pump is operating; (vi) a first control reservoir configured to store fluid removed from the dialysis circuit by the control pump and configured to store fluid that can be added to the dialysis circuit by the control pump; and (vii) one or more controllers for controlling a rate of the control pump, a rate of the blood pump, and a rate of the dialysate pump. a hemodialysis system having: (i) a controlled compliance dialysis circuit having a substantially inflexible volume; (ii) an extracorporeal circuit having a conduit for receiving blood from a subject and a conduit for returning blood to the subject, and a blood pump for conveying blood from the subject, to the dialyzer and back to the subject; and (iii) a dialyzer with a dialysis membrane wherein blood and a dialysate contact different sides of the dialysis membrane, a blood inlet end for receiving blood, a blood outlet end for allowing blood out of the dialyzer, a dialysate inlet end for receiving dialysate and a dialysate outlet end for allowing dialysate out of the dialyzer; (i) a controlled compliance dialysis circuit having a substantially inflexible volume; (ii) an extracorporeal circuit having a conduit for receiving blood from a subject and a conduit for returning blood to the subject, and a blood pump for conveying blood from the subject, to the dialyzer and back to the subject; and (iii) a dialyzer with a dialysis membrane wherein blood and a dialysate contact different sides of the dialysis membrane, a blood inlet end for receiving blood, a blood outlet end for allowing blood out of the dialyzer, a dialysate inlet end for receiving dialysate and a dialysate outlet end for allowing dialysate out of the dialyzer; wherein the controlled compliance dialysis circuit comprises: (iv) a dialysis circuit having a sorbent cartridge for removing at least one impurity or waste species from the dialysate, one or more conduits for conveying dialysate between the sorbent cartridge and the dialyzer, and a dialysate pump for conveying dialysate from the sorbent cartridge, to the dialyzer and back to the sorbent cartridge, the sorbent cartridge having a dialysate inlet end and a dialysate outlet end; (v) a control pump configured to move fluid bi-directionally between the dialysis circuit and the extracorporeal circuit, and where a flux of fluid moving between the extracorporeal circuit and the dialysis circuit is changed by the rate at which the control pump is operating; (vi) a first control reservoir configured to store fluid removed from the dialysis circuit by the control pump and configured to store fluid that can be added to the dialysis circuit by the control pump; and (vii) one or more controllers for controlling a rate of the control pump, a rate of the blood pump, and a rate of the dialysate pump. (iv) a dialysis circuit having a sorbent cartridge for removing at least one impurity or waste species from the dialysate, one or more conduits for conveying dialysate between the sorbent cartridge and the dialyzer, and a dialysate pump for conveying dialysate from the sorbent cartridge, to the dialyzer and back to the sorbent cartridge, the sorbent cartridge having a dialysate inlet end and a dialysate outlet end; (v) a control pump configured to move fluid bi-directionally between the dialysis circuit and the extracorporeal circuit, and where a flux of fluid moving between the extracorporeal circuit and the dialysis circuit is changed by the rate at which the control pump is operating; (vi) a first control reservoir configured to store fluid removed from the dialysis circuit by the control pump and configured to store fluid that can be added to the dialysis circuit by the control pump; and (vii) one or more controllers for controlling a rate of the control pump, a rate of the blood pump, and a rate of the dialysate pump.