The spindle assembly is of the type having a spool upon which coils of strand material are formed preparatory to doffing of a strand package from the assembly. The coils are formed without overlapping them upon one another, and preferably without permitting their transverse engagement and possible mutual attachment. First and second oppositely directed helical grooves are respectively provided upon upper and lower portions of the spool. The first groove prevents overlapping and transverse attachment of the strand material as the coils are formed. Both grooves position strand material at a location favorable to clearance from the spool.