diff --git a/putty.h b/putty.h
index 0726d057..975b4504 100644
--- a/putty.h
+++ b/putty.h
@@ -1709,6 +1709,8 @@ void random_setup_special();
 /* Manually drop a random seed into the random number generator, e.g.
  * just before generating a key. */
 void random_reseed(ptrlen seed);
+/* Limit on how much entropy is worth putting into the generator (bits). */
+size_t random_seed_bits(void);
 
 /*
  * Exports from pinger.c.
diff --git a/ssh.h b/ssh.h
index 4445bed1..82539d5d 100644
--- a/ssh.h
+++ b/ssh.h
@@ -902,6 +902,7 @@ void prng_seed_begin(prng *p);
 void prng_seed_finish(prng *p);
 void prng_read(prng *p, void *vout, size_t size);
 void prng_add_entropy(prng *p, unsigned source_id, ptrlen data);
+size_t prng_seed_bits(prng *p);
 
 /* This function must be implemented by the platform, and returns a
  * timer in milliseconds that the PRNG can use to know whether it's
diff --git a/sshprng.c b/sshprng.c
index ee1e0df2..ea40c99f 100644
--- a/sshprng.c
+++ b/sshprng.c
@@ -284,3 +284,9 @@ void prng_add_entropy(prng *pr, unsigned source_id, ptrlen data)
         prng_seed_finish(&pi->Prng);
     }
 }
+
+size_t prng_seed_bits(prng *pr)
+{
+    prng_impl *pi = container_of(pr, prng_impl, Prng);
+    return pi->hashalg->hlen * 8;
+}
diff --git a/sshrand.c b/sshrand.c
index 292956e4..994c7cfc 100644
--- a/sshrand.c
+++ b/sshrand.c
@@ -123,4 +123,10 @@ void random_get_savedata(void **data, int *len)
     *data = buf;
 }
 
+size_t random_seed_bits(void)
+{
+    assert(random_active > 0);
+    return prng_seed_bits(global_prng);
+}
+
 #endif /* FUZZING */
diff --git a/windows/winpgen.c b/windows/winpgen.c
index 7f6a232a..818bc728 100644
--- a/windows/winpgen.c
+++ b/windows/winpgen.c
@@ -1166,6 +1166,12 @@ static INT_PTR CALLBACK MainDlgProc(HWND hwnd, UINT msg,
                 else
                     raw_entropy_required = 256;
 
+                /* Bound the entropy collection above by the amount of
+                 * data we can actually fit into the PRNG. Any more
+                 * than that and it's doing no more good. */
+                if (raw_entropy_required > random_seed_bits())
+                    raw_entropy_required = random_seed_bits();
+
                 raw_entropy_buf = snewn(raw_entropy_required, unsigned char);
                 if (win_read_random(raw_entropy_buf, raw_entropy_required)) {
                     /*