diff --git a/chain/src/types.rs b/chain/src/types.rs
index 560458d0..a6a1c3fc 100644
--- a/chain/src/types.rs
+++ b/chain/src/types.rs
@@ -70,7 +70,7 @@ impl Tip {
 			height: 0,
 			last_block_h: gbh,
 			prev_block_h: gbh,
-			total_difficulty: Difficulty::one(),
+			total_difficulty: Difficulty::min(),
 		}
 	}
 
diff --git a/chain/tests/store_indices.rs b/chain/tests/store_indices.rs
index f4ae5a16..1d74b607 100644
--- a/chain/tests/store_indices.rs
+++ b/chain/tests/store_indices.rs
@@ -53,7 +53,7 @@ fn test_various_store_indices() {
 	let genesis = pow::mine_genesis_block().unwrap();
 	let reward = libtx::reward::output(&keychain, &key_id, 0, 1).unwrap();
 
-	let block = Block::new(&genesis.header, vec![], Difficulty::one(), reward).unwrap();
+	let block = Block::new(&genesis.header, vec![], Difficulty::min(), reward).unwrap();
 	let block_hash = block.hash();
 
 	{
diff --git a/core/fuzz/src/main.rs b/core/fuzz/src/main.rs
index 65c6adf0..2b623270 100644
--- a/core/fuzz/src/main.rs
+++ b/core/fuzz/src/main.rs
@@ -50,7 +50,7 @@ fn block() -> Block {
 
 	let reward = reward::output(&keychain, &key_id, 0, header.height).unwrap();
 
-	Block::new(&header, txs, Difficulty::one(), reward).unwrap()
+	Block::new(&header, txs, Difficulty::min(), reward).unwrap()
 }
 
 fn compact_block() -> CompactBlock {
diff --git a/core/src/consensus.rs b/core/src/consensus.rs
index 2ba2389a..d903d1a8 100644
--- a/core/src/consensus.rs
+++ b/core/src/consensus.rs
@@ -290,8 +290,8 @@ where
 		BLOCK_TIME_WINDOW,
 		CLAMP_FACTOR,
 	);
-	// minimum of 3 avoids getting stuck due to dampening
-	let difficulty = max(3, diff_sum * BLOCK_TIME_SEC / adj_ts);
+	// minimum difficulty avoids getting stuck due to dampening
+	let difficulty = max(MIN_DIFFICULTY, diff_sum * BLOCK_TIME_SEC / adj_ts);
 
 	HeaderInfo::from_diff_scaling(Difficulty::from_num(difficulty), sec_pow_scaling)
 }
@@ -320,8 +320,8 @@ pub fn secondary_pow_scaling(height: u64, diff_data: &Vec<HeaderInfo>) -> u32 {
 	);
 	let scale = scale_sum * target_pct / adj_count;
 
-	// minimum of 3 avoids getting stuck due to dampening
-	max(3, min(scale, MAX_SECONDARY_SCALING)) as u32
+	// minimum difficulty avoids getting stuck due to dampening
+	max(MIN_DIFFICULTY, min(scale, MAX_SECONDARY_SCALING)) as u32
 }
 
 /// Consensus rule that collections of items are sorted lexicographically.
diff --git a/core/src/genesis.rs b/core/src/genesis.rs
index d2994fcf..cb4e88d3 100644
--- a/core/src/genesis.rs
+++ b/core/src/genesis.rs
@@ -44,7 +44,7 @@ pub fn genesis_testnet1() -> core::Block {
 		height: 0,
 		timestamp: Utc.ymd(2017, 11, 16).and_hms(20, 0, 0),
 		pow: ProofOfWork {
-			total_difficulty: Difficulty::one(),
+			total_difficulty: Difficulty::min(),
 			scaling_difficulty: 1,
 			nonce: 28205,
 			proof: Proof::new(vec![
diff --git a/core/src/pow/types.rs b/core/src/pow/types.rs
index 6c4e143e..b4fff5b6 100644
--- a/core/src/pow/types.rs
+++ b/core/src/pow/types.rs
@@ -236,7 +236,7 @@ impl Default for ProofOfWork {
 	fn default() -> ProofOfWork {
 		let proof_size = global::proofsize();
 		ProofOfWork {
-			total_difficulty: Difficulty::one(),
+			total_difficulty: Difficulty::min(),
 			scaling_difficulty: 1,
 			nonce: 0,
 			proof: Proof::zero(proof_size),
diff --git a/core/tests/common/mod.rs b/core/tests/common/mod.rs
index 66222a34..b9604642 100644
--- a/core/tests/common/mod.rs
+++ b/core/tests/common/mod.rs
@@ -92,7 +92,7 @@ where
 	Block::new(
 		&previous_header,
 		txs.into_iter().cloned().collect(),
-		Difficulty::one(),
+		Difficulty::min(),
 		reward_output,
 	).unwrap()
 }
diff --git a/core/tests/consensus.rs b/core/tests/consensus.rs
index 47855997..9dc5108c 100644
--- a/core/tests/consensus.rs
+++ b/core/tests/consensus.rs
@@ -381,7 +381,6 @@ fn adjustment_scenarios() {
 fn next_target_adjustment() {
 	global::set_mining_mode(global::ChainTypes::AutomatedTesting);
 	let cur_time = Utc::now().timestamp() as u64;
-	let diff_one = Difficulty::one();
 	let diff_min = Difficulty::min();
 
 	// Check we don't get stuck on difficulty <= MIN_DIFFICULTY (at 4x faster blocks at least)
diff --git a/p2p/src/serv.rs b/p2p/src/serv.rs
index b53bf893..a194ace2 100644
--- a/p2p/src/serv.rs
+++ b/p2p/src/serv.rs
@@ -232,7 +232,7 @@ pub struct DummyAdapter {}
 
 impl ChainAdapter for DummyAdapter {
 	fn total_difficulty(&self) -> Difficulty {
-		Difficulty::one()
+		Difficulty::min()
 	}
 	fn total_height(&self) -> u64 {
 		0
diff --git a/p2p/tests/peer_handshake.rs b/p2p/tests/peer_handshake.rs
index 44ca7c76..e1afc30e 100644
--- a/p2p/tests/peer_handshake.rs
+++ b/p2p/tests/peer_handshake.rs
@@ -75,7 +75,7 @@ fn peer_handshake() {
 	let mut peer = Peer::connect(
 		&mut socket,
 		p2p::Capabilities::UNKNOWN,
-		Difficulty::one(),
+		Difficulty::min(),
 		my_addr,
 		&p2p::handshake::Handshake::new(Hash::from_vec(&vec![]), p2p_config.clone()),
 		net_adapter,
@@ -86,10 +86,10 @@ fn peer_handshake() {
 	peer.start(socket);
 	thread::sleep(time::Duration::from_secs(1));
 
-	peer.send_ping(Difficulty::one(), 0).unwrap();
+	peer.send_ping(Difficulty::min(), 0).unwrap();
 	thread::sleep(time::Duration::from_secs(1));
 
 	let server_peer = server.peers.get_connected_peer(&my_addr).unwrap();
-	assert_eq!(server_peer.info.total_difficulty(), Difficulty::one());
+	assert_eq!(server_peer.info.total_difficulty(), Difficulty::min());
 	assert!(server.peers.peer_count() > 0);
 }
diff --git a/pool/tests/block_building.rs b/pool/tests/block_building.rs
index 4ffc54cd..960651f1 100644
--- a/pool/tests/block_building.rs
+++ b/pool/tests/block_building.rs
@@ -54,7 +54,7 @@ fn test_transaction_pool_block_building() {
 		let key_id = ExtKeychain::derive_key_id(1, height as u32, 0, 0, 0);
 		let fee = txs.iter().map(|x| x.fee()).sum();
 		let reward = libtx::reward::output(&keychain, &key_id, fee, height).unwrap();
-		let block = Block::new(&prev_header, txs, Difficulty::one(), reward).unwrap();
+		let block = Block::new(&prev_header, txs, Difficulty::min(), reward).unwrap();
 
 		chain.update_db_for_block(&block);
 		block.header
@@ -115,7 +115,7 @@ fn test_transaction_pool_block_building() {
 		let key_id = ExtKeychain::derive_key_id(1, 2, 0, 0, 0);
 		let fees = txs.iter().map(|tx| tx.fee()).sum();
 		let reward = libtx::reward::output(&keychain, &key_id, fees, 0).unwrap();
-		Block::new(&header, txs, Difficulty::one(), reward)
+		Block::new(&header, txs, Difficulty::min(), reward)
 	}.unwrap();
 
 	chain.update_db_for_block(&block);
diff --git a/pool/tests/block_reconciliation.rs b/pool/tests/block_reconciliation.rs
index e204efa5..f626f0d0 100644
--- a/pool/tests/block_reconciliation.rs
+++ b/pool/tests/block_reconciliation.rs
@@ -52,7 +52,7 @@ fn test_transaction_pool_block_reconciliation() {
 		let height = 1;
 		let key_id = ExtKeychain::derive_key_id(1, height as u32, 0, 0, 0);
 		let reward = libtx::reward::output(&keychain, &key_id, 0, height).unwrap();
-		let block = Block::new(&BlockHeader::default(), vec![], Difficulty::one(), reward).unwrap();
+		let block = Block::new(&BlockHeader::default(), vec![], Difficulty::min(), reward).unwrap();
 
 		chain.update_db_for_block(&block);
 
@@ -67,7 +67,7 @@ fn test_transaction_pool_block_reconciliation() {
 		let key_id = ExtKeychain::derive_key_id(1, 2, 0, 0, 0);
 		let fees = initial_tx.fee();
 		let reward = libtx::reward::output(&keychain, &key_id, fees, 0).unwrap();
-		let block = Block::new(&header, vec![initial_tx], Difficulty::one(), reward).unwrap();
+		let block = Block::new(&header, vec![initial_tx], Difficulty::min(), reward).unwrap();
 
 		chain.update_db_for_block(&block);
 
@@ -157,7 +157,7 @@ fn test_transaction_pool_block_reconciliation() {
 		let key_id = ExtKeychain::derive_key_id(1, 3, 0, 0, 0);
 		let fees = block_txs.iter().map(|tx| tx.fee()).sum();
 		let reward = libtx::reward::output(&keychain, &key_id, fees, 0).unwrap();
-		let block = Block::new(&header, block_txs, Difficulty::one(), reward).unwrap();
+		let block = Block::new(&header, block_txs, Difficulty::min(), reward).unwrap();
 
 		chain.update_db_for_block(&block);
 		block
diff --git a/pool/tests/transaction_pool.rs b/pool/tests/transaction_pool.rs
index eced1590..d8faf892 100644
--- a/pool/tests/transaction_pool.rs
+++ b/pool/tests/transaction_pool.rs
@@ -53,7 +53,7 @@ fn test_the_transaction_pool() {
 		let key_id = ExtKeychain::derive_key_id(1, height as u32, 0, 0, 0);
 		let reward = libtx::reward::output(&keychain, &key_id, 0, height).unwrap();
 		let mut block =
-			Block::new(&BlockHeader::default(), vec![], Difficulty::one(), reward).unwrap();
+			Block::new(&BlockHeader::default(), vec![], Difficulty::min(), reward).unwrap();
 
 		chain.update_db_for_block(&block);