A tubular string includes a first tubular member with a pin end with pin threads and a pin external load shoulder. The tubular string also includes a second tubular member with a box end with a box external load shoulder and box threads, the pin threads being threadable into the box threads to form a connection, wherein the pin external load shoulder has an outer diameter (OD) that is different than an OD of the box external load shoulder. A load distribution sleeve is locatable between the first and second tubular members when threaded together and includes a first end facing the first tubular member and a second end facing the second tubular member, wherein the ODs of the load distribution sleeve first and second ends match the ODs of the pin and box external load shoulders respectively. The load distribution sleeve contacts the pin and box external load shoulders and distributes a make-up load between the pin and box external load shoulders when the connection is made up.