A method of making a strike construction for a pick tool, the strike construction comprising: a strike tip and a support body, in which respective attachment ends (10, 22) of each of the strike tip and support body are joined to each other, the attachment end of the strike tip is coterminous with cemented carbide material comprised in the strike tip, and the attachment end of the support body is coterminous with cemented carbide material comprised in an end portion of the support body, the end portion being configured such that sides of the support body depend divergently from its attachment end; the method including: providing the strike tip and a precursor body for the support body, in which a proximate end of the precursor body is coterminous with cemented carbide material comprised in an end portion of the precursor body, the end portion of the precursor body being configured such that sides of the precursor body depend divergently from its proximate end, the area of which is less than the area of the attachment end of the support body and the end portion of the precursor body is at least slightly longer than that of the support body; processing the end portion of the precursor body by grinding or cutting away material from adjacent the proximate end of the precursor body, thus shortening the end portion and increasing the area of the proximate end to that of the attachment end of the support body; and then joining the respective attachment ends (10, 22) of the strike tip and the support body to provide the strike construction; wherein the strike construction includes an exposed edge defined by an intersection of an attachment end of the support body and a side area adjacent the attachment end of the strike tip, and the method includes subsequently processing the exposed edge to form an arcuate edge area in which the arcuate edge area defines an osculating circle having a radius of at least 0.01 millimeters. a strike tip and a support body, in which respective attachment ends (10, 22) of each of the strike tip and support body are joined to each other, the attachment end of the strike tip is coterminous with cemented carbide material comprised in the strike tip, and the attachment end of the support body is coterminous with cemented carbide material comprised in an end portion of the support body, the end portion being configured such that sides of the support body depend divergently from its attachment end; providing the strike tip and a precursor body for the support body, in which a proximate end of the precursor body is coterminous with cemented carbide material comprised in an end portion of the precursor body, the end portion of the precursor body being configured such that sides of the precursor body depend divergently from its proximate end, the area of which is less than the area of the attachment end of the support body and the end portion of the precursor body is at least slightly longer than that of the support body; processing the end portion of the precursor body by grinding or cutting away material from adjacent the proximate end of the precursor body, thus shortening the end portion and increasing the area of the proximate end to that of the attachment end of the support body; and then joining the respective attachment ends (10, 22) of the strike tip and the support body to provide the strike construction; wherein the strike construction includes an exposed edge defined by an intersection of an attachment end of the support body and a side area adjacent the attachment end of the strike tip, and the method includes subsequently processing the exposed edge to form an arcuate edge area in which the arcuate edge area defines an osculating circle having a radius of at least 0.01 millimeters.