'anxiety-reducing' is a compound of 'anxiety' and 'reducing'. 'anxiety' originates from Latin, specifically the word 'anxietas' (from 'anxius'), where 'anxius' meant 'troubled' or 'uneasy'; 'reduce' originates from Latin, specifically the word 'reducere', where 're-' meant 'back' and 'ducere' meant 'to lead'.

'anxiety' came into English via Old French 'anxieté' and Middle English 'anxieté'/'anxiety'; 'reduce' passed from Latin 'reducere' into Old French 'reduire' and then into Middle English as 'reduce'.

Initially, 'anxiety' referred broadly to anguish or uneasy concern, a sense that has largely persisted; 'reduce' originally carried the sense 'lead back' but evolved to mean 'make smaller or lessen', which is the sense used in the compound 'anxiety-reducing'.