--- a/src/dane-openssl.c
+++ b/src/dane-openssl.c
@@ -1098,8 +1098,8 @@ if (dane->selectors[DANESSL_USAGE_DANE_T
      * Check that setting the untrusted chain updates the expected
      * structure member at the expected offset.
      */
-    X509_STORE_CTX_trusted_stack(ctx, dane->roots);
-    X509_STORE_CTX_set_chain(ctx, dane->chain);
+    X509_STORE_CTX_set0_trusted_stack(ctx, dane->roots);
+    X509_STORE_CTX_set0_untrusted(ctx, dane->chain);
     OPENSSL_assert(dane->chain == X509_STORE_CTX_get0_untrusted(ctx));
     }
   }
--- a/src/pdkim/signing.c
+++ b/src/pdkim/signing.c
@@ -703,7 +703,6 @@ return NULL;
 void
 exim_dkim_init(void)
 {
-ERR_load_crypto_strings();
 }
 
 
--- a/src/tls-openssl.c
+++ b/src/tls-openssl.c
@@ -22,7 +22,10 @@ functions from the OpenSSL library. */
 #include <openssl/lhash.h>
 #include <openssl/ssl.h>
 #include <openssl/err.h>
+#include <openssl/bn.h>
+#include <openssl/dh.h>
 #include <openssl/rand.h>
+#include <openssl/rsa.h>
 #ifndef OPENSSL_NO_ECDH
 # include <openssl/ec.h>
 #endif
@@ -885,8 +888,9 @@ pkey = EVP_RSA_gen(2048);
 
 X509_set_version(x509, 2);				/* N+1 - version 3 */
 ASN1_INTEGER_set(X509_get_serialNumber(x509), 1);
-X509_gmtime_adj(X509_get_notBefore(x509), 0);
-X509_gmtime_adj(X509_get_notAfter(x509), (long)2 * 60 * 60);	/* 2 hour */
+X509_gmtime_adj(X509_getm_notBefore(x509), 0);
+X509_gmtime_adj(X509_getm_notAfter(x509), (long)2 * 60 * 60);	/* 2 hour */
+
 X509_set_pubkey(x509, pkey);
 
 name = X509_get_subject_name(x509);
@@ -4670,8 +4674,8 @@ return string_fmt_append(g,
     "                          Runtime: %s\n"
     "                                 : %s\n",
 	     OPENSSL_VERSION_TEXT,
-	     SSLeay_version(SSLEAY_VERSION),
-	     SSLeay_version(SSLEAY_BUILT_ON));
+	     OpenSSL_version(OPENSSL_VERSION),
+	     OpenSSL_version(OPENSSL_BUILT_ON));
   /* third line is 38 characters for the %s and the line is 73 chars long;
   the OpenSSL output includes a "built on: " prefix already. */
 }
@@ -4713,8 +4717,6 @@ if (pidnow != pidlast)
   is unique for each thread", this doesn't apparently apply across processes,
   so our own warning from vaguely_random_number_fallback() applies here too.
   Fix per PostgreSQL. */
-  if (pidlast != 0)
-    RAND_cleanup();
   pidlast = pidnow;
   }
 
--- a/src/tlscert-openssl.c
+++ b/src/tlscert-openssl.c
@@ -218,13 +218,13 @@ return mod ? tls_field_from_dn(cp, mod)
 uschar *
 tls_cert_not_before(void * cert, uschar * mod)
 {
-return asn1_time_copy(X509_get_notBefore((X509 *)cert), mod);
+return asn1_time_copy(X509_getm_notBefore((X509 *)cert), mod);
 }
 
 uschar *
 tls_cert_not_after(void * cert, uschar * mod)
 {
-return asn1_time_copy(X509_get_notAfter((X509 *)cert), mod);
+return asn1_time_copy(X509_getm_notAfter((X509 *)cert), mod);
 }
 
 uschar *