Head engagement and membrane sweep?

I went to my antenatal, and the baby's head is now 'brim'. Which is a progression from 'free'.

However it's not engaged yet.

Will they do a membrane sweep next week if it's still the same way?

The midwife was unsure, she said she personally would but doesn't know about the other midwives who may be on shift.

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Answer:
I had a membrane sweep exactly 7 days past my due date. That was the earliest time i could have one.. I was 2cm dilated at that point so i dont know if thats why my midwife gave me one. My baby's head was brim too…it never “engaged”. If you do have a sweep it works wonders… after mine i felt a bit crampy walking bk from my appointment and went into labour that same night!!! Had my little boy 9 days late! good luck x

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Answer:
my midwife booked me in for a membrane sweep 2 days before my due date but luckily i went into labour on the day it was booked for!!(baby mustve known what was coming!)…our babies head didnt engage until last min which is perfectly normal.I guess it would depend on your midwife but personally i would try go without & let things happen naturally.