diff --git a/crypto/crypto.c b/crypto/crypto.c
index 390cd8b..9f4639f 100644
--- a/crypto/crypto.c
+++ b/crypto/crypto.c
@@ -40,6 +40,18 @@
                                OPENSSL_ARM || OPENSSL_AARCH64) */
 
 
+// Our assembly does not use the GOT to reference symbols, which means
+// references to visible symbols will often require a TEXTREL. This is
+// undesirable, so all assembly-referenced symbols should be hidden. CPU
+// capabilities are the only such symbols defined in C. Explicitly hide them,
+// rather than rely on being built with -fvisibility=hidden.
+#if defined(OPENSSL_WINDOWS)
+#define HIDDEN
+#else
+#define HIDDEN __attribute__((visibility("hidden")))
+#endif
+
+
 // The capability variables are defined in this file in order to work around a
 // linker bug. When linking with a .a, if no symbols in a .o are referenced
 // then the .o is discarded, even if it has constructor functions.
@@ -57,11 +69,11 @@
 // archive, linking on OS X will fail to resolve common symbols. By
 // initialising it to zero, it becomes a "data symbol", which isn't so
 // affected.
-uint32_t OPENSSL_ia32cap_P[4] = {0};
+HIDDEN uint32_t OPENSSL_ia32cap_P[4] = {0};
 
 #elif defined(OPENSSL_PPC64LE)
 
-unsigned long OPENSSL_ppc64le_hwcap2 = 0;
+HIDDEN unsigned long OPENSSL_ppc64le_hwcap2 = 0;
 
 #elif defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64)
 
@@ -69,7 +81,7 @@
 
 #if defined(OPENSSL_STATIC_ARMCAP)
 
-uint32_t OPENSSL_armcap_P =
+HIDDEN uint32_t OPENSSL_armcap_P =
 #if defined(OPENSSL_STATIC_ARMCAP_NEON) || defined(__ARM_NEON__)
     ARMV7_NEON |
 #endif
@@ -88,7 +100,7 @@
     0;
 
 #else
-uint32_t OPENSSL_armcap_P = 0;
+HIDDEN uint32_t OPENSSL_armcap_P = 0;
 #endif
 
 #endif
diff --git a/crypto/fipsmodule/bn/asm/armv4-mont.pl b/crypto/fipsmodule/bn/asm/armv4-mont.pl
index c2020cc..9d0926a 100644
--- a/crypto/fipsmodule/bn/asm/armv4-mont.pl
+++ b/crypto/fipsmodule/bn/asm/armv4-mont.pl
@@ -740,7 +740,6 @@
 .align	2
 #if __ARM_MAX_ARCH__>=7
 .comm	OPENSSL_armcap_P,4,4
-.hidden	OPENSSL_armcap_P
 #endif
 ___
 
diff --git a/crypto/fipsmodule/sha/asm/sha1-armv4-large.pl b/crypto/fipsmodule/sha/asm/sha1-armv4-large.pl
index 27187dd..d52fa4e 100644
--- a/crypto/fipsmodule/sha/asm/sha1-armv4-large.pl
+++ b/crypto/fipsmodule/sha/asm/sha1-armv4-large.pl
@@ -698,7 +698,6 @@
 $code.=<<___;
 #if __ARM_MAX_ARCH__>=7
 .comm	OPENSSL_armcap_P,4,4
-.hidden	OPENSSL_armcap_P
 #endif
 ___
 
diff --git a/crypto/fipsmodule/sha/asm/sha256-armv4.pl b/crypto/fipsmodule/sha/asm/sha256-armv4.pl
index 3eea080..3694b2b 100644
--- a/crypto/fipsmodule/sha/asm/sha256-armv4.pl
+++ b/crypto/fipsmodule/sha/asm/sha256-armv4.pl
@@ -684,7 +684,6 @@
 .align	2
 #if __ARM_MAX_ARCH__>=7 && !defined(__KERNEL__)
 .comm   OPENSSL_armcap_P,4,4
-.hidden OPENSSL_armcap_P
 #endif
 ___
 
diff --git a/crypto/fipsmodule/sha/asm/sha512-armv4.pl b/crypto/fipsmodule/sha/asm/sha512-armv4.pl
index 85f403e..6cafcf6 100644
--- a/crypto/fipsmodule/sha/asm/sha512-armv4.pl
+++ b/crypto/fipsmodule/sha/asm/sha512-armv4.pl
@@ -649,7 +649,6 @@
 .align	2
 #if __ARM_MAX_ARCH__>=7 && !defined(__KERNEL__)
 .comm	OPENSSL_armcap_P,4,4
-.hidden	OPENSSL_armcap_P
 #endif
 ___
 
diff --git a/crypto/perlasm/x86_64-xlate.pl b/crypto/perlasm/x86_64-xlate.pl
index 37240b2..60a5c64 100755
--- a/crypto/perlasm/x86_64-xlate.pl
+++ b/crypto/perlasm/x86_64-xlate.pl
@@ -753,11 +753,7 @@
 		$self->{value} = $dir . "\t" . $$line;
 
 		if ($dir =~ /\.extern/) {
-		    if ($flavour eq "elf") {
-			$self->{value} .= "\n.hidden $$line";
-		    } else {
-			$self->{value} = "";
-		    }
+		    $self->{value} = ""; # swallow extern
 		} elsif (!$elf && $dir =~ /\.type/) {
 		    $self->{value} = "";
 		    $self->{value} = ".def\t" . ($globals{$1} or $1) . ";\t" .