It's possible that what you consider contact is too light. It's one of those judgements that make lessons with a good instructor so worthwhile: you need to know what you're looking for; and also where schooling exercises sometimes DIFFER from the ideal showing-time exercise.
Long-and-low is no good if it's on loose reins. I think it's not unusual, when you start, that your horse will take a very strong contact, but I think it's okay. You can work with that. It's much harder if your horse dips his head and starts prancing: by doing that he's refusing to "be" with you.