Compiler warning on unused exception...need to improve structure? Consider the below:

public int DoSomethingComplicated(ComplicatedObject input)
{
    try {
        return input.Analyse();
    }
    catch(CustomExceptionOne ex1)
    {
         throw;
    }
    catch(CustomExceptionTwo ex2)
    {
         Log(ex2.Message);
         return -1;
    }
}


Obviously I have abstracted quite a bit for the example, but the idea is that the try block performs a task which can cause one of two types of runtime exception. 

In the event that the exception type is CustomExceptionOne, I want to simply throw the exception. For CustomExceptionTwo on the other hand, I want to log the issue but return -1.

I do not have access to the input.Analyse() method in order to change it.

This all looks fine to me, and works fine, but I get a compiler warning because ex1 is technically never used. I don't really want to throw the entire ex1 exception, so I am wondering how I can get this warning to go away.

I can think of a couple of hacky ways like Console.WriteLine(ex1.Message) or something but that isn't a route I particularly want to go down.
You can refactor your code the following way:

public int DoSomethingComplicated(ComplicatedObject input)
{
    try 
    {
        return input.Analyse();
    }
    catch(CustomExceptionTwo ex2)
    {
         Log(ex2.Message);
         return -1;
    }
}


throw; re-throws the same exception, so there is no point in such catch block. 

Alternatively, you can use catch(CustomExceptionOne) syntax.