diff --git a/src/test/util_tests.cpp b/src/test/util_tests.cpp
index f56969cba68..1b0ccad5118 100644
--- a/src/test/util_tests.cpp
+++ b/src/test/util_tests.cpp
@@ -261,4 +261,66 @@ BOOST_AUTO_TEST_CASE(util_IsHex)
     BOOST_CHECK(!IsHex("0x0000"));
 }
 
+BOOST_AUTO_TEST_CASE(util_seed_insecure_rand)
+{
+    // Expected results for the determinstic seed.
+    const uint32_t exp_vals[11] = {  91632771U,1889679809U,3842137544U,3256031132U,
+                                   1761911779U, 489223532U,2692793790U,2737472863U,
+                                   2796262275U,1309899767U,840571781U};
+    // Expected 0s in rand()%(idx+2) for the determinstic seed.
+    const int exp_count[9] = {5013,3346,2415,1972,1644,1386,1176,1096,1009};
+    int i;
+    int count=0;
+
+    seed_insecure_rand();
+
+    //Does the non-determistic rand give us results that look too like the determinstic one?
+    for (i=0;i<10;i++)
+    {
+        int match = 0;
+        uint32_t rval = insecure_rand();
+        for (int j=0;j<11;j++)match |= rval==exp_vals[j];
+        count += match;
+    }
+    // sum(binomial(10,i)*(11/(2^32))^i*(1-(11/(2^32)))^(10-i),i,0,4) ~= 1-1/2^134.73
+    // So _very_ unlikely to throw a false failure here.
+    BOOST_CHECK(count<=4);
+
+    for (int mod=2;mod<11;mod++)
+    {
+        int mask = 1;
+        // Really rough binomal confidence approximation.
+        int err = 30*10000./mod*sqrt((1./mod*(1-1./mod))/10000.);
+        //mask is 2^ceil(log2(mod))-1
+        while(mask<mod-1)mask=(mask<<1)+1;
+
+        count = 0;
+        //How often does it get a zero from the uniform range [0,mod)?
+        for (i=0;i<10000;i++)
+        {
+            uint32_t rval;
+            do{
+                rval=insecure_rand()&mask;
+            }while(rval>=(uint32_t)mod);
+            count += rval==0;
+        }
+        BOOST_CHECK(count<=10000/mod+err);
+        BOOST_CHECK(count>=10000/mod-err);
+    }
+
+    seed_insecure_rand(true);
+
+    for (i=0;i<11;i++)
+    {
+        BOOST_CHECK_EQUAL(insecure_rand(),exp_vals[i]);
+    }
+
+    for (int mod=2;mod<11;mod++)
+    {
+        count = 0;
+        for (i=0;i<10000;i++) count += insecure_rand()%mod==0;
+        BOOST_CHECK_EQUAL(count,exp_count[mod-2]);
+    }
+}
+
 BOOST_AUTO_TEST_SUITE_END()
diff --git a/src/util.cpp b/src/util.cpp
index d8f05cb9fd2..49ac3510f3a 100644
--- a/src/util.cpp
+++ b/src/util.cpp
@@ -1276,12 +1276,26 @@ void AddTimeData(const CNetAddr& ip, int64 nTime)
     }
 }
 
-
-
-
-
-
-
+uint32_t insecure_rand_Rz = 11;
+uint32_t insecure_rand_Rw = 11;
+void seed_insecure_rand(bool fDeterministic)
+{
+    //The seed values have some unlikely fixed points which we avoid.
+    if(fDeterministic)
+    {
+        insecure_rand_Rz = insecure_rand_Rw = 11;
+    } else {
+        uint32_t tmp;
+        do{
+            RAND_bytes((unsigned char*)&tmp,4);
+        }while(tmp==0 || tmp==0x9068ffffU);
+        insecure_rand_Rz=tmp;
+        do{
+            RAND_bytes((unsigned char*)&tmp,4);
+        }while(tmp==0 || tmp==0x464fffffU);
+        insecure_rand_Rw=tmp;
+    }
+}
 
 string FormatVersion(int nVersion)
 {
diff --git a/src/util.h b/src/util.h
index 97911d7493e..5cdca37e8b3 100644
--- a/src/util.h
+++ b/src/util.h
@@ -403,13 +403,27 @@ bool SoftSetArg(const std::string& strArg, const std::string& strValue);
  */
 bool SoftSetBoolArg(const std::string& strArg, bool fValue);
 
+/**
+ * MWC RNG of George Marsaglia
+ * This is intended to be fast. It has a period of 2^59.3, though the
+ * least significant 16 bits only have a period of about 2^30.1.
+ *
+ * @return random value
+ */
+extern uint32_t insecure_rand_Rz;
+extern uint32_t insecure_rand_Rw;
+static inline uint32_t insecure_rand(void)
+{
+  insecure_rand_Rz=36969*(insecure_rand_Rz&65535)+(insecure_rand_Rz>>16);
+  insecure_rand_Rw=18000*(insecure_rand_Rw&65535)+(insecure_rand_Rw>>16);
+  return (insecure_rand_Rw<<16)+insecure_rand_Rz;
+}
 
-
-
-
-
-
-
+/**
+ * Seed insecure_rand using the random pool.
+ * @param Deterministic Use a determinstic seed
+ */
+void seed_insecure_rand(bool fDeterministic=false);
 
 /** Median filter over a stream of values.
  * Returns the median of the last N numbers
diff --git a/src/wallet.cpp b/src/wallet.cpp
index 2317ac31ac7..067473d0875 100644
--- a/src/wallet.cpp
+++ b/src/wallet.cpp
@@ -973,6 +973,8 @@ static void ApproximateBestSubset(vector<pair<int64, pair<const CWalletTx*,unsig
     vfBest.assign(vValue.size(), true);
     nBest = nTotalLower;
 
+    seed_insecure_rand();
+
     for (int nRep = 0; nRep < iterations && nBest != nTargetValue; nRep++)
     {
         vfIncluded.assign(vValue.size(), false);
@@ -982,7 +984,13 @@ static void ApproximateBestSubset(vector<pair<int64, pair<const CWalletTx*,unsig
         {
             for (unsigned int i = 0; i < vValue.size(); i++)
             {
-                if (nPass == 0 ? rand() % 2 : !vfIncluded[i])
+                //The solver here uses a randomized algorithm,
+                //the randomness serves no real security purpose but is just
+                //needed to prevent degenerate behavior and it is important
+                //that the rng fast. We do not use a constant random sequence,
+                //because there may be some privacy improvement by making
+                //the selection random.
+                if (nPass == 0 ? insecure_rand()&1 : !vfIncluded[i])
                 {
                     nTotal += vValue[i].first;
                     vfIncluded[i] = true;