Sophie, my DH also had poor count (<1million the first time we tested), motility and morphology.
Aside from all the normal hormone tests, the only other tests that he had to determine possible cause were a blood test for the DAZ gene (which is a hereditary cause of low sperm count), and a quick feel by my FS for any obvious abnormalities.

We ended up falling pg via IUI (after a failed IVF cycle), so DH and I were so pleased to see that his swimmers had some life in them

It was possibly coincidental, but my DH's 3 SA's results were <1 million, 4 million, and 15 million (the IUI results). Since the first test, DH had started taking zinc supplements, and exercising vigorously (he was already fit and slim build).