A method for making a transparent compound optical flow cell (30, 30', 30") of the type used to characterize formed bodies passing through the flow cell, the optical flow cell having formed therein a rectilinear internal flow channel, the method comprising the steps of: providing a cylindrical monolithic preform (31, 31', 31") comprising a glass tube having an axially-extending channel (32, 32', 32") therethrough and a transition temperature, the channel comprising a substantially uniform original cross-section of a desired shape; heating the preform to a predetermined temperature above the transition temperature of the glass tube; axially drawing the preform at a controlled rate, for a controlled time, and at a constant angular orientation, to achieve a desired reduced cross-sectional area of the axially-extending channel; providing an optical element (37, 37', 37"), the optical element comprising a conforming surface that conforms to a segment of the drawn preform; assembling the optical element on the segment so that the optical element and the segment are in a desired spatial relationship; and optically joining the optical element to the segment so as to fix the optical element and the segment in the desired spatial relationship; characterized in that the optical element (37, 37', 37") further comprises an exterior non-cylindrical envelope of predetermined form and orientation relative to the conforming surface; and in that in the step of assembling the optical element on the segment the conforming surface of the optical element is positioned so as to minimize non-axisymmetric refractive effects on optical characterizing parameters acquired from formed bodies passing through the reduced cross-sectional area of the axially-extending channel. providing a cylindrical monolithic preform (31, 31', 31") comprising a glass tube having an axially-extending channel (32, 32', 32") therethrough and a transition temperature, the channel comprising a substantially uniform original cross-section of a desired shape; heating the preform to a predetermined temperature above the transition temperature of the glass tube; axially drawing the preform at a controlled rate, for a controlled time, and at a constant angular orientation, to achieve a desired reduced cross-sectional area of the axially-extending channel; providing an optical element (37, 37', 37"), the optical element comprising a conforming surface that conforms to a segment of the drawn preform; assembling the optical element on the segment so that the optical element and the segment are in a desired spatial relationship; and optically joining the optical element to the segment so as to fix the optical element and the segment in the desired spatial relationship; characterized in that the optical element (37, 37', 37") further comprises an exterior non-cylindrical envelope of predetermined form and orientation relative to the conforming surface; and in that in the step of assembling the optical element on the segment the conforming surface of the optical element is positioned so as to minimize non-axisymmetric refractive effects on optical characterizing parameters acquired from formed bodies passing through the reduced cross-sectional area of the axially-extending channel.