diff --git a/docs/examples/threaded-ssl.c b/docs/examples/threaded-ssl.c
index 522f8c49a..f6083ab3d 100644
--- a/docs/examples/threaded-ssl.c
+++ b/docs/examples/threaded-ssl.c
@@ -29,7 +29,7 @@
  * (libgcrypt) so far.
  *
  * OpenSSL docs for this:
- *   https://www.openssl.org/docs/crypto/threads.html
+ *   https://www.openssl.org/docs/man1.0.2/man3/CRYPTO_num_locks.html
  * gcrypt docs for this:
  *   https://gnupg.org/documentation/manuals/gcrypt/Multi_002dThreading.html
  */
diff --git a/docs/libcurl/libcurl-thread.3 b/docs/libcurl/libcurl-thread.3
index ae1e387be..796a5bb59 100644
--- a/docs/libcurl/libcurl-thread.3
+++ b/docs/libcurl/libcurl-thread.3
@@ -41,14 +41,15 @@ then of course using the underlying SSL library multi-threaded and those libs
 might have their own requirements on this issue.  You may need to provide one
 or two functions to allow it to function properly:
 .IP OpenSSL
-OpenSSL 1.1.0 "can be safely used in multi-threaded applications provided that
-support for the underlying OS threading API is built-in."
+OpenSSL 1.1.0+ "can be safely used in multi-threaded applications provided that
+support for the underlying OS threading API is built-in." In that case the
+engine is used by libcurl in a way that is fully thread-safe.
 
-https://www.openssl.org/docs/manmaster/crypto/threads.html#DESCRIPTION
+https://www.openssl.org/docs/man1.1.0/man3/CRYPTO_THREAD_run_once.html#DESCRIPTION
 
 OpenSSL <= 1.0.2 the user must set callbacks.
 
-https://www.openssl.org/docs/man1.0.2/crypto/threads.html#DESCRIPTION
+https://www.openssl.org/docs/man1.0.2/man3/CRYPTO_set_locking_callback.html#DESCRIPTION
 
 https://curl.haxx.se/libcurl/c/opensslthreadlock.html
 
diff --git a/lib/vtls/openssl.c b/lib/vtls/openssl.c
index 3cdcbfeb9..1d2ec04ed 100644
--- a/lib/vtls/openssl.c
+++ b/lib/vtls/openssl.c
@@ -3280,7 +3280,6 @@ static CURLcode pkp_pin_peer_pubkey(struct Curl_easy *data, X509* cert,
     if(len1 < 1)
       break; /* failed */
 
-    /* https://www.openssl.org/docs/crypto/buffer.html */
     buff1 = temp = malloc(len1);
     if(!buff1)
       break; /* failed */
@@ -3302,7 +3301,6 @@ static CURLcode pkp_pin_peer_pubkey(struct Curl_easy *data, X509* cert,
     result = Curl_pin_peer_pubkey(data, pinnedpubkey, buff1, len1);
   } while(0);
 
-  /* https://www.openssl.org/docs/crypto/buffer.html */
   if(buff1)
     free(buff1);