diff --git a/src/main.cpp b/src/main.cpp
index d2e736d421..41fc0b8098 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -5326,7 +5326,7 @@ bool ProcessMessages(CNode* pfrom)
 }
 
 
-bool SendMessages(CNode* pto, bool fSendTrickle)
+bool SendMessages(CNode* pto)
 {
     const Consensus::Params& consensusParams = Params().GetConsensus();
     {
@@ -5368,28 +5368,17 @@ bool SendMessages(CNode* pto, bool fSendTrickle)
             return true;
 
         // Address refresh broadcast
-        static int64_t nLastRebroadcast;
-        if (!IsInitialBlockDownload() && (GetTime() - nLastRebroadcast > 24 * 60 * 60))
-        {
-            LOCK(cs_vNodes);
-            BOOST_FOREACH(CNode* pnode, vNodes)
-            {
-                // Periodically clear addrKnown to allow refresh broadcasts
-                if (nLastRebroadcast)
-                    pnode->addrKnown.reset();
-
-                // Rebroadcast our address
-                AdvertizeLocal(pnode);
-            }
-            if (!vNodes.empty())
-                nLastRebroadcast = GetTime();
+        int64_t nNow = GetTimeMicros();
+        if (!IsInitialBlockDownload() && pto->nNextLocalAddrSend < nNow) {
+            AdvertizeLocal(pto);
+            pto->nNextLocalAddrSend = PoissonNextSend(nNow, AVG_LOCAL_ADDRESS_BROADCAST_INTERVAL);
         }
 
         //
         // Message: addr
         //
-        if (fSendTrickle)
-        {
+        if (pto->nNextAddrSend < nNow) {
+            pto->nNextAddrSend = PoissonNextSend(nNow, AVG_ADDRESS_BROADCAST_INTERVAL);
             vector<CAddress> vAddr;
             vAddr.reserve(pto->vAddrToSend.size());
             BOOST_FOREACH(const CAddress& addr, pto->vAddrToSend)
@@ -5563,8 +5552,13 @@ bool SendMessages(CNode* pto, bool fSendTrickle)
         vector<CInv> vInv;
         vector<CInv> vInvWait;
         {
+            bool fSendTrickle = pto->fWhitelisted;
+            if (pto->nNextInvSend < nNow) {
+                fSendTrickle = true;
+                pto->nNextInvSend = PoissonNextSend(nNow, AVG_INVENTORY_BROADCAST_INTERVAL);
+            }
             LOCK(pto->cs_inventory);
-            vInv.reserve(pto->vInventoryToSend.size());
+            vInv.reserve(std::min<size_t>(1000, pto->vInventoryToSend.size()));
             vInvWait.reserve(pto->vInventoryToSend.size());
             BOOST_FOREACH(const CInv& inv, pto->vInventoryToSend)
             {
@@ -5604,7 +5598,7 @@ bool SendMessages(CNode* pto, bool fSendTrickle)
             pto->PushMessage(NetMsgType::INV, vInv);
 
         // Detect whether we're stalling
-        int64_t nNow = GetTimeMicros();
+        nNow = GetTimeMicros();
         if (!pto->fDisconnect && state.nStallingSince && state.nStallingSince < nNow - 1000000 * BLOCK_STALLING_TIMEOUT) {
             // Stalling only triggers when the block download window cannot move. During normal steady state,
             // the download window should be much larger than the to-be-downloaded set of blocks, so disconnection
diff --git a/src/main.h b/src/main.h
index 19623f4d96..25a0063873 100644
--- a/src/main.h
+++ b/src/main.h
@@ -87,6 +87,14 @@ static const unsigned int DATABASE_WRITE_INTERVAL = 60 * 60;
 static const unsigned int DATABASE_FLUSH_INTERVAL = 24 * 60 * 60;
 /** Maximum length of reject messages. */
 static const unsigned int MAX_REJECT_MESSAGE_LENGTH = 111;
+/** Average delay between local address broadcasts in seconds. */
+static const unsigned int AVG_LOCAL_ADDRESS_BROADCAST_INTERVAL = 24 * 24 * 60;
+/** Average delay between peer address broadcasts in seconds. */
+static const unsigned int AVG_ADDRESS_BROADCAST_INTERVAL = 30;
+/** Average delay between trickled inventory broadcasts in seconds.
+ *  Blocks, whitelisted receivers, and a random 25% of transactions bypass this. */
+static const unsigned int AVG_INVENTORY_BROADCAST_INTERVAL = 5;
+
 static const unsigned int DEFAULT_LIMITFREERELAY = 15;
 static const bool DEFAULT_RELAYPRIORITY = true;
 
@@ -197,9 +205,8 @@ bool ProcessMessages(CNode* pfrom);
  * Send queued protocol messages to be sent to a give node.
  *
  * @param[in]   pto             The node which we are sending messages to.
- * @param[in]   fSendTrickle    When true send the trickled data, otherwise trickle the data until true.
  */
-bool SendMessages(CNode* pto, bool fSendTrickle);
+bool SendMessages(CNode* pto);
 /** Run an instance of the script checking thread */
 void ThreadScriptCheck();
 /** Try to detect Partition (network isolation) attacks against us */
diff --git a/src/net.cpp b/src/net.cpp
index c5e7ece79d..e0d96a2dc8 100644
--- a/src/net.cpp
+++ b/src/net.cpp
@@ -36,6 +36,8 @@
 #include <boost/filesystem.hpp>
 #include <boost/thread.hpp>
 
+#include <math.h>
+
 // Dump addresses to peers.dat every 15 minutes (900s)
 #define DUMP_ADDRESSES_INTERVAL 900
 
@@ -1733,11 +1735,6 @@ void ThreadMessageHandler()
             }
         }
 
-        // Poll the connected nodes for messages
-        CNode* pnodeTrickle = NULL;
-        if (!vNodesCopy.empty())
-            pnodeTrickle = vNodesCopy[GetRand(vNodesCopy.size())];
-
         bool fSleep = true;
 
         BOOST_FOREACH(CNode* pnode, vNodesCopy)
@@ -1768,7 +1765,7 @@ void ThreadMessageHandler()
             {
                 TRY_LOCK(pnode->cs_vSend, lockSend);
                 if (lockSend)
-                    g_signals.SendMessages(pnode, pnode == pnodeTrickle || pnode->fWhitelisted);
+                    g_signals.SendMessages(pnode);
             }
             boost::this_thread::interruption_point();
         }
@@ -2384,6 +2381,9 @@ CNode::CNode(SOCKET hSocketIn, const CAddress& addrIn, const std::string& addrNa
     nStartingHeight = -1;
     filterInventoryKnown.reset();
     fGetAddr = false;
+    nNextLocalAddrSend = 0;
+    nNextAddrSend = 0;
+    nNextInvSend = 0;
     fRelayTxes = false;
     pfilter = new CBloomFilter();
     nPingNonceSent = 0;
@@ -2634,3 +2634,7 @@ void DumpBanlist()
     LogPrint("net", "Flushed %d banned node ips/subnets to banlist.dat  %dms\n",
              banmap.size(), GetTimeMillis() - nStart);
 }
+
+int64_t PoissonNextSend(int64_t nNow, int average_interval_seconds) {
+    return nNow + (int64_t)(log1p(GetRand(1ULL << 48) * -0.0000000000000035527136788 /* -1/2^48 */) * average_interval_seconds * -1000000.0 + 0.5);
+}
diff --git a/src/net.h b/src/net.h
index 3ed438605e..bc64571aeb 100644
--- a/src/net.h
+++ b/src/net.h
@@ -113,7 +113,7 @@ struct CNodeSignals
 {
     boost::signals2::signal<int ()> GetHeight;
     boost::signals2::signal<bool (CNode*), CombinerAll> ProcessMessages;
-    boost::signals2::signal<bool (CNode*, bool), CombinerAll> SendMessages;
+    boost::signals2::signal<bool (CNode*), CombinerAll> SendMessages;
     boost::signals2::signal<void (NodeId, const CNode*)> InitializeNode;
     boost::signals2::signal<void (NodeId)> FinalizeNode;
 };
@@ -391,6 +391,8 @@ public:
     CRollingBloomFilter addrKnown;
     bool fGetAddr;
     std::set<uint256> setKnown;
+    int64_t nNextAddrSend;
+    int64_t nNextLocalAddrSend;
 
     // inventory based relay
     CRollingBloomFilter filterInventoryKnown;
@@ -398,6 +400,7 @@ public:
     CCriticalSection cs_inventory;
     std::set<uint256> setAskFor;
     std::multimap<int64_t, CInv> mapAskFor;
+    int64_t nNextInvSend;
     // Used for headers announcements - unfiltered blocks to relay
     // Also protected by cs_inventory
     std::vector<uint256> vBlockHashesToAnnounce;
@@ -791,4 +794,7 @@ public:
 
 void DumpBanlist();
 
+/** Return a timestamp in the future (in microseconds) for exponentially distributed events. */
+int64_t PoissonNextSend(int64_t nNow, int average_interval_seconds);
+
 #endif // BITCOIN_NET_H
diff --git a/src/test/DoS_tests.cpp b/src/test/DoS_tests.cpp
index da296a0461..51d296502e 100644
--- a/src/test/DoS_tests.cpp
+++ b/src/test/DoS_tests.cpp
@@ -49,7 +49,7 @@ BOOST_AUTO_TEST_CASE(DoS_banning)
     CNode dummyNode1(INVALID_SOCKET, addr1, "", true);
     dummyNode1.nVersion = 1;
     Misbehaving(dummyNode1.GetId(), 100); // Should get banned
-    SendMessages(&dummyNode1, false);
+    SendMessages(&dummyNode1);
     BOOST_CHECK(CNode::IsBanned(addr1));
     BOOST_CHECK(!CNode::IsBanned(ip(0xa0b0c001|0x0000ff00))); // Different IP, not banned
 
@@ -57,11 +57,11 @@ BOOST_AUTO_TEST_CASE(DoS_banning)
     CNode dummyNode2(INVALID_SOCKET, addr2, "", true);
     dummyNode2.nVersion = 1;
     Misbehaving(dummyNode2.GetId(), 50);
-    SendMessages(&dummyNode2, false);
+    SendMessages(&dummyNode2);
     BOOST_CHECK(!CNode::IsBanned(addr2)); // 2 not banned yet...
     BOOST_CHECK(CNode::IsBanned(addr1));  // ... but 1 still should be
     Misbehaving(dummyNode2.GetId(), 50);
-    SendMessages(&dummyNode2, false);
+    SendMessages(&dummyNode2);
     BOOST_CHECK(CNode::IsBanned(addr2));
 }
 
@@ -73,13 +73,13 @@ BOOST_AUTO_TEST_CASE(DoS_banscore)
     CNode dummyNode1(INVALID_SOCKET, addr1, "", true);
     dummyNode1.nVersion = 1;
     Misbehaving(dummyNode1.GetId(), 100);
-    SendMessages(&dummyNode1, false);
+    SendMessages(&dummyNode1);
     BOOST_CHECK(!CNode::IsBanned(addr1));
     Misbehaving(dummyNode1.GetId(), 10);
-    SendMessages(&dummyNode1, false);
+    SendMessages(&dummyNode1);
     BOOST_CHECK(!CNode::IsBanned(addr1));
     Misbehaving(dummyNode1.GetId(), 1);
-    SendMessages(&dummyNode1, false);
+    SendMessages(&dummyNode1);
     BOOST_CHECK(CNode::IsBanned(addr1));
     mapArgs.erase("-banscore");
 }
@@ -95,7 +95,7 @@ BOOST_AUTO_TEST_CASE(DoS_bantime)
     dummyNode.nVersion = 1;
 
     Misbehaving(dummyNode.GetId(), 100);
-    SendMessages(&dummyNode, false);
+    SendMessages(&dummyNode);
     BOOST_CHECK(CNode::IsBanned(addr));
 
     SetMockTime(nStartTime+60*60);