diff --git a/src/addrman.cpp b/src/addrman.cpp
index 6cbcbed839d..db5166be446 100644
--- a/src/addrman.cpp
+++ b/src/addrman.cpp
@@ -138,7 +138,7 @@ CAddrInfo* CAddrMan::Create(const CAddress& addr, const CNetAddr& addrSource, in
     return &mapInfo[nId];
 }
 
-void CAddrMan::SwapRandom(unsigned int nRndPos1, unsigned int nRndPos2)
+void CAddrMan::SwapRandom(unsigned int nRndPos1, unsigned int nRndPos2) const
 {
     AssertLockHeld(cs);
 
@@ -150,11 +150,13 @@ void CAddrMan::SwapRandom(unsigned int nRndPos1, unsigned int nRndPos2)
     int nId1 = vRandom[nRndPos1];
     int nId2 = vRandom[nRndPos2];
 
-    assert(mapInfo.count(nId1) == 1);
-    assert(mapInfo.count(nId2) == 1);
+    const auto it_1{mapInfo.find(nId1)};
+    const auto it_2{mapInfo.find(nId2)};
+    assert(it_1 != mapInfo.end());
+    assert(it_2 != mapInfo.end());
 
-    mapInfo[nId1].nRandomPos = nRndPos2;
-    mapInfo[nId2].nRandomPos = nRndPos1;
+    it_1->second.nRandomPos = nRndPos2;
+    it_2->second.nRandomPos = nRndPos1;
 
     vRandom[nRndPos1] = nId2;
     vRandom[nRndPos2] = nId1;
@@ -541,7 +543,7 @@ int CAddrMan::Check_()
 }
 #endif
 
-void CAddrMan::GetAddr_(std::vector<CAddress>& vAddr, size_t max_addresses, size_t max_pct, std::optional<Network> network)
+void CAddrMan::GetAddr_(std::vector<CAddress>& vAddr, size_t max_addresses, size_t max_pct, std::optional<Network> network) const
 {
     AssertLockHeld(cs);
 
@@ -561,9 +563,10 @@ void CAddrMan::GetAddr_(std::vector<CAddress>& vAddr, size_t max_addresses, size
 
         int nRndPos = insecure_rand.randrange(vRandom.size() - n) + n;
         SwapRandom(n, nRndPos);
-        assert(mapInfo.count(vRandom[n]) == 1);
+        const auto it{mapInfo.find(vRandom[n])};
+        assert(it != mapInfo.end());
 
-        const CAddrInfo& ai = mapInfo[vRandom[n]];
+        const CAddrInfo& ai{it->second};
 
         // Filter by network (optional)
         if (network != std::nullopt && ai.GetNetClass() != network) continue;
diff --git a/src/addrman.h b/src/addrman.h
index 02b8c5d9a2f..d4f67c2f5b1 100644
--- a/src/addrman.h
+++ b/src/addrman.h
@@ -55,7 +55,7 @@ private:
     bool fInTried{false};
 
     //! position in vRandom
-    int nRandomPos{-1};
+    mutable int nRandomPos{-1};
 
     friend class CAddrMan;
 
@@ -596,7 +596,7 @@ public:
      * @param[in] max_pct        Maximum percentage of addresses to return (0 = all).
      * @param[in] network        Select only addresses of this network (nullopt = all).
      */
-    std::vector<CAddress> GetAddr(size_t max_addresses, size_t max_pct, std::optional<Network> network)
+    std::vector<CAddress> GetAddr(size_t max_addresses, size_t max_pct, std::optional<Network> network) const
         EXCLUSIVE_LOCKS_REQUIRED(!cs)
     {
         LOCK(cs);
@@ -669,7 +669,9 @@ private:
     std::unordered_map<CNetAddr, int, CNetAddrHash> mapAddr GUARDED_BY(cs);
 
     //! randomly-ordered vector of all nIds
-    std::vector<int> vRandom GUARDED_BY(cs);
+    //! This is mutable because it is unobservable outside the class, so any
+    //! changes to it (even in const methods) are also unobservable.
+    mutable std::vector<int> vRandom GUARDED_BY(cs);
 
     // number of "tried" entries
     int nTried GUARDED_BY(cs);
@@ -697,7 +699,7 @@ private:
     CAddrInfo* Create(const CAddress &addr, const CNetAddr &addrSource, int *pnId = nullptr) EXCLUSIVE_LOCKS_REQUIRED(cs);
 
     //! Swap two elements in vRandom.
-    void SwapRandom(unsigned int nRandomPos1, unsigned int nRandomPos2) EXCLUSIVE_LOCKS_REQUIRED(cs);
+    void SwapRandom(unsigned int nRandomPos1, unsigned int nRandomPos2) const EXCLUSIVE_LOCKS_REQUIRED(cs);
 
     //! Move an entry from the "new" table(s) to the "tried" table
     void MakeTried(CAddrInfo& info, int nId) EXCLUSIVE_LOCKS_REQUIRED(cs);
@@ -752,7 +754,7 @@ private:
      * @param[in] max_pct        Maximum percentage of addresses to return (0 = all).
      * @param[in] network        Select only addresses of this network (nullopt = all).
      */
-    void GetAddr_(std::vector<CAddress>& vAddr, size_t max_addresses, size_t max_pct, std::optional<Network> network) EXCLUSIVE_LOCKS_REQUIRED(cs);
+    void GetAddr_(std::vector<CAddress>& vAddr, size_t max_addresses, size_t max_pct, std::optional<Network> network) const EXCLUSIVE_LOCKS_REQUIRED(cs);
 
     /** We have successfully connected to this peer. Calling this function
      *  updates the CAddress's nTime, which is used in our IsTerrible()