After a Three of a Suit Opening/Overcall

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The Principles for Responder's 1st Round Bid

Simplex Principles of 1st Round Responses to Three of a Suit

PRINCIPLE 9: Simplex is a fundamentally natural bidding system. The only gadgets used are 2♣ Redshift, 4NT Blackwood, and the Simplex 2NT.
PRINCIPLE 10: Responding hands with trump support but less than 10 HCP bid immediately to their total trump level. (For example, after a 1♥ opening by partner, a hand containing 6 HCP and four cards in the heart suit would immediately raise to 3♥. Partner is known to have at least five hearts. Add those five to the four that responder has makes nine. Take six from nine means a raise to the 3-level.) Equally if opener has less than 10 HCP but support for responder's suit, he will bid to the total trump level on the second round.
PRINCIPLE 11: If a bidder cannot make the first-round bid his hand merits (because the opposition have already taken the auction too high), the bidder simply doubles, with an implied message to partner: "RHO has just taken my opening bid away, and I believe it is safe for you to bid at this or one level higher."
PRINCIPLE 13: Ignore first-round doubles by the opponents. Carry on and make the bid you would have made if the opponents had passed.
PRINCIPLE 18: An opening bid, overcall or response of Three of a new Suit guarantees four or more cards in the suit and 17-22 HCP.
PRINCIPLE 22: Always bid the cheaper of two equal-length suits.
PRINCIPLE 23: Except for strong (17+ HCP) hands and responses to doubles, four-card suits are never explicitly bid in the first round.

Box R1A (Version 1.0)	Responding to One of a Suit (1♣, 1♦, 1♥, 1♠)
Bid	Meaning	Forcing?	Where to next?
Pass	0-7 HCP and less than 3-card support for partner's suit	NF
Double	Unable even to bid 1NT. RHO's overcall has taken his bid away.	NF	Box O2A
One of a New Suit	5+ cards, 8-16 points, compliant with Rule of 18.	NF	Box O2B
1NT	8-16 HCP and no other available bid — i.e. the 'dustbin' bid. The hand will contain fewer than four cards in opener's suit. The hand may contain four cards in another suit, or a 5-card suit not now biddable at the 1-level.	NF	Box O2B
Two of a New Suit	6+ cards and 3-16 points	NF	Box O2B
Raise to Two of the Suit	3-card support and 0-9 HCP	NF	Box O2C
2NT	4+ card support and 10+ HCP	F	Box O2B
Three of a New Suit	4+ cards and 17+ HCP	GF	Box O2B
Raise to Three of the Suit	4-card support and 0-9 HCP	NF	Box O2D
Raise to Four of the Suit	5-card support and 0-9 HCP	NF	Box O2E
Raise to Five of Opener's Minor	6+card support and 0-9 HCP	NF	Box O2F