(1) Background: Tooth extraction is one of the oldest and most well-known surgical procedures in dental medicine. It is still routinely performed to date by both general practitioners, oral surgeons, and dental undergraduates. The Benex extraction system allows for the extraction of teeth in vertical direction, which avoids most trauma against the surrounding alveolar bone and soft tissues; (2) Methods: The study included 56 patients who were recruited from the department of Oral Surgery at the Faculty of Dental Medicine, Medical University – Plovdiv. Patients were divided into two groups of 28 patients – Group I (control group) and Group II (study group). For each group the success of the extraction, buccal cortical plate preservation, pain experience and early wound healing were assessed; (3) Results: There was no statistical significance between the success of the extractions in both groups. The Benex extractions preserved the buccal cortical plate in 95% of the cases, whereas the forceps extractions only in 71.8%, which shows a statistical significance. On the seventh day patients in group II reported less pain, without a significant difference. There was a significantly bigger number of completely healed extraction wounds on the 10th day; (4) Conclusions: Atraumatic extractions allow for more hard and soft tissues to be preserved in the extraction site. This is all crucial for the successful outcome and aesthetically pleasing results of a following prosthetic or implant restoration.