This paper investigates trade balances and unit values focusing on Hungarian-Slovenian bilateral agri-food trade flows to distinguish types of one-way and two-way trade flows, categories of price competition and categories of quality competition. We combine Gehlhar — Pick’s (GP) (2002) procedure of four trade categories with knowledge from literature on intra-industry trade (IIT) to disentangle one-way trade, which can be significant when trade between two countries is imbalanced, from two-way matched trade flows with unit values as proxies for price. By comparing the empirical results obtained using the additional categories of one-way trade and disentangled IIT types in two-way matched trade by product was found that GP’s two price and two quality competition categories and IIT types complement each other. The decomposition of GP non-price competition categories on quality competition and one-way trade illustrates that one-way trade is the most significant component of agri-food trade between Hungary and Slovenia, a finding relevant for agri-food trade of several small countries. One-way trade cannot be associated by the simultaneous export and import unit values by the product, but by some other factors of trade specialisation and comparative trade advantages of relevance for public policy makers and private business.