This paper presents the findings of a research project which aimed to contribute to the social inclusion of people with intellectual disabilities (ID) in the WWW. The Inclusive New Media Design (INMD) project brought together 31 web designers and developers with 29 people with intellectual disabilities to explore the best practice for building websites accessible to the ID community. Specifically, the project took accessibility techniques identified in ID accessibility research, and investigated what would (or would not) make it possible for web professionals to implement them. This paper suggests some tentative answers to the question of whether a fully accessible web can be built, one that includes people with ID. While the paper outlines simple steps that can be taken to facilitate accessibility for people at the mild end of the ID spectrum, it also highlights a number of barriers that exist to implementing ID accessibility guidance, most notably the power-holders and decision-makers with whom web designers work, who may not share the designers’ commitment to accessibility.