Cough suppression can be described as a decreased desire and need to cough.   This is typically regarded as a positive effect which helps alleviate a pre-existing ailment. In certain contexts, it can also allow an individual to inhale much larger amounts of smoke than they would usually be able to, without accompanying pain or the desire to cough. However, it is worth noting that the efficacy of many over the counter cough medication is questionable, particularly in children. 
Cough suppression is most commonly induced under the influence of moderate dosages of antitussive compounds such as codeine  , pholcodine, dextromethorphan  , noscapine, and butamirate. However, it may also occur under the influence of certain antihistamines such as promethazine.
- Smith, S. M., Schroeder, K., & Fahey, T. (2014). Over-the-counter (OTC) medications for acute cough in children and adults in community settings. | https://doi.org/10.1002/14651858.CD001831.pub5
- Malesker, M. A., Callahan-Lyon, P., Ireland, B., Irwin, R. S., Adams, T. M., Altman, K. W., ... & Bolser, D. C. (2017). Pharmacologic and Nonpharmacologic Treatment for Acute Cough Associated With the Common Cold: CHEST Expert Panel Report. Chest, 152(5), 1021-1037. | https://www.ncbi.nlm.nih.gov/pubmed/28837801
- MINUTES OF THE 2nd COUGH AND COLD REVIEW GROUP MEETING | https://web.archive.org/web/20100525060232/http://www.medsafe.govt.nz/hot/alerts/CoughandCold/Minutes2CoughandCold.asp
- Bolser, D. C., & Davenport, P. W. (2007). Codeine and cough: an ineffective gold standard. Current opinion in allergy and clinical immunology, 7(1), 32. | https://doi.org/10.1016/j.chest.2017.08.009
- DeAlleaume, L., & Tweed, E. M. (2009). Do OTC remedies relieve cough in acute URIs?. Clinical Inquiries, 2009 (MU). | https://www.ncbi.nlm.nih.gov/pubmed/19874728