On 2014–01–09 Jean-Guillaume wrote:

> In the subsection head, I would like to suppress the newline between the
> number and the text,

That's controlled by the “after” key.

 \setuphead
  [Exercise]
  [after=]

> My purpose is to define something like:
> 
>  \definehead[Exercise][subsection]
>  \setuphead
>   [Exercise]
>   [alternative=Mine?,
>   ...,
>   numberstyle=bold]

Please provide full working examples next time. That makes it easier
for us and it's more likely you'll get a response.

> So I can typeset a list of exercises in a compact way. I could use
> enumerations but I don't think I should.

That depends on your document. You can use sections, enumerations or
Wolfgang's annotation module.

Marco