Legal and non-legal scholarship examines extensively the impact of subjective conditions such as biases on international judicial decision-making. This paper shifts the focus on the impact of objective conditions on international judicial decision-making with similar effects and introduces the concept of ‘unneutrality’ as a model for investigating such conditions. Specifically, the unneutrality of international adjudication requires the anchoring of decisive arguments in basic legal concepts and ideals, which constrains decision-making and leads to the appearance of favouring certain stakeholders. Considering that different legal interpretations and outcomes are often attributed to biases, the paper hypothesizes that what is usually perceived as an appearance of bias is reflected in the anchoring of decisive arguments in basic legal concepts and ideals with direct effects on outcomes. The paper reviews a sample of decisions rendered by the European Court of Human Rights and investment treaty arbitral tribunals dealing with jurisdictional matters, and finds a direct link between anchors and outcomes, whose favourability to certain stakeholders is often alleged to reflect biases. While the choice of anchors can be influenced by subjective conditions such as biases, the need for a choice is rather objective. The paper therefore suggests that the study of international judicial decision-making should take into account the impact of objective conditions relating to the structural attributes of the international legal order, and their ability to produce the effects that have been so far attributed almost exclusively to subjective conditions