diff --git a/CHANGELOG_PENDING.md b/CHANGELOG_PENDING.md
index 419c4640a..028ea17f6 100644
--- a/CHANGELOG_PENDING.md
+++ b/CHANGELOG_PENDING.md
@@ -25,3 +25,4 @@ Friendly reminder, we have a [bug bounty program](https://hackerone.com/tendermi
 
 ### BUG FIXES:
 
+- [blockchain/v1] [\#5701](https://github.com/tendermint/tendermint/pull/5701) Handle peers without blocks (@melekes)
diff --git a/blockchain/v1/peer.go b/blockchain/v1/peer.go
index ad26585b3..a9b5e0379 100644
--- a/blockchain/v1/peer.go
+++ b/blockchain/v1/peer.go
@@ -31,6 +31,7 @@ type BpPeer struct {
 	Height                  int64                  // the peer reported height
 	NumPendingBlockRequests int                    // number of requests still waiting for block responses
 	blocks                  map[int64]*types.Block // blocks received or expected to be received from this peer
+	noBlocks                map[int64]struct{}     // heights for which the peer does not have blocks
 	blockResponseTimer      *time.Timer
 	recvMonitor             *flow.Monitor
 	params                  *BpPeerParams // parameters for timer and monitor
@@ -46,13 +47,14 @@ func NewBpPeer(peerID p2p.ID, base int64, height int64,
 		params = BpPeerDefaultParams()
 	}
 	return &BpPeer{
-		ID:     peerID,
-		Base:   base,
-		Height: height,
-		blocks: make(map[int64]*types.Block, maxRequestsPerPeer),
-		logger: log.NewNopLogger(),
-		onErr:  onErr,
-		params: params,
+		ID:       peerID,
+		Base:     base,
+		Height:   height,
+		blocks:   make(map[int64]*types.Block, maxRequestsPerPeer),
+		noBlocks: make(map[int64]struct{}),
+		logger:   log.NewNopLogger(),
+		onErr:    onErr,
+		params:   params,
 	}
 }
 
@@ -131,6 +133,19 @@ func (peer *BpPeer) RemoveBlock(height int64) {
 	delete(peer.blocks, height)
 }
 
+// SetNoBlock records that the peer does not have a block for height.
+func (peer *BpPeer) SetNoBlock(height int64) {
+	peer.noBlocks[height] = struct{}{}
+}
+
+// NoBlock returns true if the peer does not have a block for height.
+func (peer *BpPeer) NoBlock(height int64) bool {
+	if _, ok := peer.noBlocks[height]; ok {
+		return true
+	}
+	return false
+}
+
 // RequestSent records that a request was sent, and starts the peer timer and monitor if needed.
 func (peer *BpPeer) RequestSent(height int64) {
 	peer.blocks[height] = nil
diff --git a/blockchain/v1/pool.go b/blockchain/v1/pool.go
index 27e0f3a04..9c037183d 100644
--- a/blockchain/v1/pool.go
+++ b/blockchain/v1/pool.go
@@ -100,6 +100,18 @@ func (pool *BlockPool) UpdatePeer(peerID p2p.ID, base int64, height int64) error
 	return nil
 }
 
+// SetNoBlock records that the peer does not have a block for height and
+// schedules a new request for that height from another peer.
+func (pool *BlockPool) SetNoBlock(peerID p2p.ID, height int64) {
+	peer := pool.peers[peerID]
+	if peer == nil {
+		return
+	}
+	peer.SetNoBlock(height)
+
+	pool.rescheduleRequest(peerID, height)
+}
+
 // Cleans and deletes the peer. Recomputes the max peer height.
 func (pool *BlockPool) deletePeer(peer *BpPeer) {
 	if peer == nil {
@@ -214,7 +226,7 @@ func (pool *BlockPool) sendRequest(height int64) bool {
 		if peer.NumPendingBlockRequests >= maxRequestsPerPeer {
 			continue
 		}
-		if peer.Base > height || peer.Height < height {
+		if peer.Base > height || peer.Height < height || peer.NoBlock(height) {
 			continue
 		}
 
diff --git a/blockchain/v1/reactor_fsm.go b/blockchain/v1/reactor_fsm.go
index 61f74b916..33f9a9102 100644
--- a/blockchain/v1/reactor_fsm.go
+++ b/blockchain/v1/reactor_fsm.go
@@ -277,6 +277,7 @@ func init() {
 				return waitForBlock, err
 			case noBlockResponseEv:
 				fsm.logger.Error("peer does not have requested block", "peer", data.peerID)
+				fsm.pool.SetNoBlock(data.peerID, data.height)
 
 				return waitForBlock, nil
 			case processedBlockEv:
diff --git a/blockchain/v1/reactor_fsm_test.go b/blockchain/v1/reactor_fsm_test.go
index 99b8d378d..9fdfe9c9b 100644
--- a/blockchain/v1/reactor_fsm_test.go
+++ b/blockchain/v1/reactor_fsm_test.go
@@ -102,6 +102,19 @@ func sProcessedBlockEv(current, expected string, reactorError error) fsmStepTest
 	}
 }
 
+func sNoBlockResponseEv(current, expected string, peerID p2p.ID, height int64, err error) fsmStepTestValues {
+	return fsmStepTestValues{
+		currentState: current,
+		event:        noBlockResponseEv,
+		data: bReactorEventData{
+			peerID: peerID,
+			height: height,
+		},
+		wantState: expected,
+		wantErr:   err,
+	}
+}
+
 func sStatusEv(current, expected string, peerID p2p.ID, height int64, err error) fsmStepTestValues {
 	return fsmStepTestValues{
 		currentState: current,
@@ -354,6 +367,46 @@ func TestFSMBlockVerificationFailure(t *testing.T) {
 	executeFSMTests(t, tests, false)
 }
 
+func TestFSMNoBlockResponse(t *testing.T) {
+	tests := []testFields{
+		{
+			name:               "no block response",
+			startingHeight:     1,
+			maxRequestsPerPeer: 3,
+			steps: []fsmStepTestValues{
+				sStartFSMEv(),
+
+				// add P1 and get blocks 1-3 from it
+				sStatusEv("waitForPeer", "waitForBlock", "P1", 3, nil),
+				sMakeRequestsEv("waitForBlock", "waitForBlock", maxNumRequests),
+				sBlockRespEv("waitForBlock", "waitForBlock", "P1", 1, []int64{}),
+				sBlockRespEv("waitForBlock", "waitForBlock", "P1", 2, []int64{1}),
+				sBlockRespEv("waitForBlock", "waitForBlock", "P1", 3, []int64{1, 2}),
+
+				// add P2
+				sStatusEv("waitForBlock", "waitForBlock", "P2", 3, nil),
+
+				// process block failure, should remove P1 and all blocks
+				sNoBlockResponseEv("waitForBlock", "waitForBlock", "P1", 1, nil),
+				sNoBlockResponseEv("waitForBlock", "waitForBlock", "P1", 2, nil),
+				sNoBlockResponseEv("waitForBlock", "waitForBlock", "P1", 3, nil),
+
+				// get blocks 1-3 from P2
+				sMakeRequestsEv("waitForBlock", "waitForBlock", maxNumRequests),
+				sBlockRespEv("waitForBlock", "waitForBlock", "P2", 1, []int64{}),
+				sBlockRespEv("waitForBlock", "waitForBlock", "P2", 2, []int64{1}),
+				sBlockRespEv("waitForBlock", "waitForBlock", "P2", 3, []int64{1, 2}),
+
+				// finish after processing blocks 1 and 2
+				sProcessedBlockEv("waitForBlock", "waitForBlock", nil),
+				sProcessedBlockEv("waitForBlock", "finished", nil),
+			},
+		},
+	}
+
+	executeFSMTests(t, tests, false)
+}
+
 func TestFSMBadBlockFromPeer(t *testing.T) {
 	tests := []testFields{
 		{