A high tracheostomy may be indicated in-
Scleroma of the larynx
Multiple papillomatosis of larynx
Bilateral vocal cord paralysis
Carcinoma of larynx
“It is important (in tracheostomy) to refrain from causing any damage in the region of cricoid cartilage.
An exception to this rule is when a patient has laryngeal malignancy and under these circumstances tracheostomy should be placed high so as to allow resection of tracheostomy site at the time of laryngectomy”. 
“ The high tracheostomy is generally avoided because of the postoperative risk of peri-chondritis of the cricoid cartilage and subglottic stenosis. In cases of carcinoma larynx with stridor when total laryn-gectomy would be done, high tracheostomy is indicated.”