I was just looking into this because we're thinking about TTC, and I'd be 36 when the baby came... Maybe some of this will be helpful to somebody.
Nuchal fold catches 60-80% of chromosone abnormal babies. Privately (not with NHS) you can get a combined nuchal fold-blood test (2 biophysical markers) also around 12 weeks. Cost in the region of £200. You can pay more to get the quadruple test (4 biophysical markers) around 16 weeks. There are places which will feed all the results from the 2 blood tests+nuchal fold+your age into a computer to calculate your risk.
And they still only catch about 85% of the chromosone abnormal babies. Ultrasound might catch another 5-7% looking for "soft markers".
So that means 8-10% of chromosone defect babies that just can't be detected without invasive testing.
Also, CVS sometimes comes up with an ambiguous result: CVS can find Mosaic trisomy (partial chromosone duplications) in the placenta. But only the placenta may have the problem; the trisomy may not be in the baby at all. So you would still have to have an amnio to know for sure.
Against that you have to consider risks of CVS/amnio; in addition to miscarriage they may just manage to puncture the baby during an amnio and cause physical damage, including brain damage (see AIMS website). A woman even died in the UK from sepsis following an amnio. I have the impression that if amniotic fluid gets into a woman's blood stream that would also be fatal.
Moreover, something like 3% of all birth defects cannot be detected with amnio. Occasionally an amnio has to be redone because insufficient fluid is withdrawn. I've heard it can take 3 weeks for full amnio results to come back in some health authorities; which would take most of us to at least 19 wks pregnant. Who would want to terminate so late?
Not a nice lot of options, is it??