diff --git a/src/main.cpp b/src/main.cpp
index 4a28bbb00..61d9301f8 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -5569,18 +5569,11 @@ public:
         mp = mempool;
     }
 
-    bool operator()(const CInv &a, const CInv &b)
+    bool operator()(std::set<uint256>::iterator a, std::set<uint256>::iterator b)
     {
-        if (a.type != MSG_TX && b.type != MSG_TX) {
-            return false;
-        } else {
-            if (a.type != MSG_TX) {
-                return true;
-            } else if (b.type != MSG_TX) {
-                return false;
-            }
-            return mp->CompareDepthAndScore(a.hash, b.hash);
-        }
+        /* As std::make_heap produces a max-heap, we want the entries with the
+         * fewest ancestors/highest fee to sort later. */
+        return mp->CompareDepthAndScore(*b, *a);
     }
 };
 
@@ -5808,38 +5801,59 @@ bool SendMessages(CNode* pto)
         // Message: inventory
         //
         vector<CInv> vInv;
-        vector<CInv> vInvWait;
         {
+            LOCK(pto->cs_inventory);
+            vInv.reserve(std::max<size_t>(pto->vInventoryBlockToSend.size(), INVENTORY_BROADCAST_MAX));
+
+            // Add blocks
+            BOOST_FOREACH(const uint256& hash, pto->vInventoryBlockToSend) {
+                vInv.push_back(CInv(MSG_BLOCK, hash));
+                if (vInv.size() == MAX_INV_SZ) {
+                    pto->PushMessage(NetMsgType::INV, vInv);
+                    vInv.clear();
+                }
+            }
+            pto->vInventoryBlockToSend.clear();
+
+            // Determine transactions to relay
             bool fSendTrickle = pto->fWhitelisted;
             if (pto->nNextInvSend < nNow) {
                 fSendTrickle = true;
-                // Use half the delay for outbound peers, as their is less privacy concern for them.
+                // Use half the delay for outbound peers, as there is less privacy concern for them.
                 pto->nNextInvSend = PoissonNextSend(nNow, INVENTORY_BROADCAST_INTERVAL >> !pto->fInbound);
             }
-            LOCK(pto->cs_inventory);
-            if (fSendTrickle && pto->vInventoryToSend.size() > 1) {
+            if (fSendTrickle) {
+                // Produce a vector with all candidates for sending
+                vector<std::set<uint256>::iterator> vInvTx;
+                vInvTx.reserve(pto->setInventoryTxToSend.size());
+                for (std::set<uint256>::iterator it = pto->setInventoryTxToSend.begin(); it != pto->setInventoryTxToSend.end(); it++) {
+                    vInvTx.push_back(it);
+                }
                 // Topologically and fee-rate sort the inventory we send for privacy and priority reasons.
+                // A heap is used so that not all items need sorting if only a few are being sent.
                 CompareInvMempoolOrder compareInvMempoolOrder(&mempool);
-                std::stable_sort(pto->vInventoryToSend.begin(), pto->vInventoryToSend.end(), compareInvMempoolOrder);
-            }
-            vInv.reserve(std::min<size_t>(INVENTORY_BROADCAST_MAX, pto->vInventoryToSend.size()));
-            vInvWait.reserve(pto->vInventoryToSend.size());
-            BOOST_FOREACH(const CInv& inv, pto->vInventoryToSend)
-            {
-                if (inv.type == MSG_TX && pto->filterInventoryKnown.contains(inv.hash))
-                    continue;
+                std::make_heap(vInvTx.begin(), vInvTx.end(), compareInvMempoolOrder);
                 // No reason to drain out at many times the network's capacity,
                 // especially since we have many peers and some will draw much shorter delays.
-                if (vInv.size() >= INVENTORY_BROADCAST_MAX || (inv.type == MSG_TX && !fSendTrickle)) {
-                    vInvWait.push_back(inv);
-                    continue;
+                unsigned int nRelayedTransactions = 0;
+                while (!vInvTx.empty() && nRelayedTransactions < INVENTORY_BROADCAST_MAX) {
+                    // Fetch the top element from the heap
+                    std::pop_heap(vInvTx.begin(), vInvTx.end(), compareInvMempoolOrder);
+                    std::set<uint256>::iterator it = vInvTx.back();
+                    vInvTx.pop_back();
+                    uint256 hash = *it;
+                    // Remove it from the to-be-sent set
+                    pto->setInventoryTxToSend.erase(it);
+                    // Check if not in the filter already
+                    if (pto->filterInventoryKnown.contains(hash)) {
+                        continue;
+                    }
+                    // Send
+                    vInv.push_back(CInv(MSG_TX, hash));
+                    nRelayedTransactions++;
+                    pto->filterInventoryKnown.insert(hash);
                 }
-
-                pto->filterInventoryKnown.insert(inv.hash);
-
-                vInv.push_back(inv);
             }
-            pto->vInventoryToSend = vInvWait;
         }
         if (!vInv.empty())
             pto->PushMessage(NetMsgType::INV, vInv);
diff --git a/src/net.h b/src/net.h
index bf367684f..a95fa79e7 100644
--- a/src/net.h
+++ b/src/net.h
@@ -397,7 +397,13 @@ public:
 
     // inventory based relay
     CRollingBloomFilter filterInventoryKnown;
-    std::vector<CInv> vInventoryToSend;
+    // Set of transaction ids we still have to announce.
+    // They are sorted by the mempool before relay, so the order is not important.
+    std::set<uint256> setInventoryTxToSend;
+    // List of block ids we still have announce.
+    // There is no final sorting before sending, as they are always sent immediately
+    // and in the order requested.
+    std::vector<uint256> vInventoryBlockToSend;
     CCriticalSection cs_inventory;
     std::set<uint256> setAskFor;
     std::multimap<int64_t, CInv> mapAskFor;
@@ -517,11 +523,13 @@ public:
 
     void PushInventory(const CInv& inv)
     {
-        {
-            LOCK(cs_inventory);
-            if (inv.type == MSG_TX && filterInventoryKnown.contains(inv.hash))
-                return;
-            vInventoryToSend.push_back(inv);
+        LOCK(cs_inventory);
+        if (inv.type == MSG_TX) {
+            if (!filterInventoryKnown.contains(inv.hash)) {
+                setInventoryTxToSend.insert(inv.hash);
+            }
+        } else if (inv.type == MSG_BLOCK) {
+            vInventoryBlockToSend.push_back(inv.hash);
         }
     }