diff --git a/CMakeLists.txt b/CMakeLists.txt
index fdabd9f7..11928406 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -697,7 +697,7 @@ if(XZ_SMALL)
     target_sources(liblzma PRIVATE src/liblzma/check/crc32_small.c)
 else()
     target_sources(liblzma PRIVATE
-        src/liblzma/check/crc32_table.c
+        src/liblzma/check/crc32_fast.c
         src/liblzma/check/crc32_table_be.h
         src/liblzma/check/crc32_table_le.h
     )
@@ -705,8 +705,6 @@ else()
     if(XZ_ASM_I386)
         target_sources(liblzma PRIVATE src/liblzma/check/crc32_x86.S)
         target_compile_definitions(liblzma PRIVATE HAVE_CRC_X86_ASM)
-    else()
-        target_sources(liblzma PRIVATE src/liblzma/check/crc32_fast.c)
     endif()
 endif()
 
@@ -717,7 +715,7 @@ if("crc64" IN_LIST XZ_CHECKS)
         target_sources(liblzma PRIVATE src/liblzma/check/crc64_small.c)
     else()
         target_sources(liblzma PRIVATE
-            src/liblzma/check/crc64_table.c
+            src/liblzma/check/crc64_fast.c
             src/liblzma/check/crc64_table_be.h
             src/liblzma/check/crc64_table_le.h
         )
@@ -726,8 +724,6 @@ if("crc64" IN_LIST XZ_CHECKS)
             target_sources(liblzma PRIVATE src/liblzma/check/crc64_x86.S)
             # Adding #define HAVE_CRC_X86_ASM was already handled in
             # the CRC32 case a few lines above. CRC32 is always built.
-        else()
-            target_sources(liblzma PRIVATE src/liblzma/check/crc64_fast.c)
         endif()
     endif()
 endif()
diff --git a/src/liblzma/check/Makefile.inc b/src/liblzma/check/Makefile.inc
index 6c0e3739..8334924c 100644
--- a/src/liblzma/check/Makefile.inc
+++ b/src/liblzma/check/Makefile.inc
@@ -20,13 +20,11 @@ if COND_SMALL
 liblzma_la_SOURCES += check/crc32_small.c
 else
 liblzma_la_SOURCES += \
-	check/crc32_table.c \
+	check/crc32_fast.c \
 	check/crc32_table_le.h \
 	check/crc32_table_be.h
 if COND_ASM_X86
 liblzma_la_SOURCES += check/crc32_x86.S
-else
-liblzma_la_SOURCES += check/crc32_fast.c
 endif
 endif
 
@@ -35,13 +33,11 @@ if COND_SMALL
 liblzma_la_SOURCES += check/crc64_small.c
 else
 liblzma_la_SOURCES += \
-	check/crc64_table.c \
+	check/crc64_fast.c \
 	check/crc64_table_le.h \
 	check/crc64_table_be.h
 if COND_ASM_X86
 liblzma_la_SOURCES += check/crc64_x86.S
-else
-liblzma_la_SOURCES += check/crc64_fast.c
 endif
 endif
 endif
diff --git a/src/liblzma/check/crc32_fast.c b/src/liblzma/check/crc32_fast.c
index 832f6c08..725a025a 100644
--- a/src/liblzma/check/crc32_fast.c
+++ b/src/liblzma/check/crc32_fast.c
@@ -28,6 +28,17 @@
 // Generic CRC32 //
 ///////////////////
 
+#ifdef WORDS_BIGENDIAN
+#	include "crc32_table_be.h"
+#else
+#	include "crc32_table_le.h"
+#endif
+
+
+#ifdef HAVE_CRC_X86_ASM
+extern uint32_t lzma_crc32_generic(
+		const uint8_t *buf, size_t size, uint32_t crc);
+#else
 static uint32_t
 lzma_crc32_generic(const uint8_t *buf, size_t size, uint32_t crc)
 {
@@ -85,7 +96,8 @@ lzma_crc32_generic(const uint8_t *buf, size_t size, uint32_t crc)
 
 	return ~crc;
 }
-#endif
+#endif // HAVE_CRC_X86_ASM
+#endif // CRC32_GENERIC
 
 
 #if defined(CRC32_GENERIC) && defined(CRC32_ARCH_OPTIMIZED)
diff --git a/src/liblzma/check/crc32_table.c b/src/liblzma/check/crc32_table.c
deleted file mode 100644
index 56413eec..00000000
--- a/src/liblzma/check/crc32_table.c
+++ /dev/null
@@ -1,42 +0,0 @@
-// SPDX-License-Identifier: 0BSD
-
-///////////////////////////////////////////////////////////////////////////////
-//
-/// \file       crc32_table.c
-/// \brief      Precalculated CRC32 table with correct endianness
-//
-//  Author:     Lasse Collin
-//
-///////////////////////////////////////////////////////////////////////////////
-
-#include "common.h"
-
-
-// FIXME: Compared to crc_common.h this has to check for __x86_64__ too
-// so that in 32-bit builds crc32_x86.S won't break due to a missing table.
-#if defined(HAVE_USABLE_CLMUL) && ((defined(__x86_64__) && defined(__SSSE3__) \
-			&& defined(__SSE4_1__) && defined(__PCLMUL__)) \
-		|| (defined(__e2k__) && __iset__ >= 6))
-#	define NO_CRC32_TABLE
-
-#elif defined(HAVE_ARM64_CRC32) \
-		&& !defined(WORDS_BIGENDIAN) \
-		&& defined(__ARM_FEATURE_CRC32)
-#	define NO_CRC32_TABLE
-#endif
-
-
-#if !defined(HAVE_ENCODERS) && defined(NO_CRC32_TABLE)
-// No table needed. Use a typedef to avoid an empty translation unit.
-typedef void lzma_crc32_dummy;
-
-#else
-// Having the declaration here silences clang -Wmissing-variable-declarations.
-extern const uint32_t lzma_crc32_table[8][256];
-
-#	ifdef WORDS_BIGENDIAN
-#		include "crc32_table_be.h"
-#	else
-#		include "crc32_table_le.h"
-#	endif
-#endif
diff --git a/src/liblzma/check/crc32_x86.S b/src/liblzma/check/crc32_x86.S
index ddc3cee6..37ee063d 100644
--- a/src/liblzma/check/crc32_x86.S
+++ b/src/liblzma/check/crc32_x86.S
@@ -67,7 +67,7 @@ init_table(void)
 #endif
 #define MAKE_SYM_CAT(prefix, sym) prefix ## sym
 #define MAKE_SYM(prefix, sym) MAKE_SYM_CAT(prefix, sym)
-#define LZMA_CRC32 MAKE_SYM(__USER_LABEL_PREFIX__, lzma_crc32)
+#define LZMA_CRC32 MAKE_SYM(__USER_LABEL_PREFIX__, lzma_crc32_generic)
 #define LZMA_CRC32_TABLE MAKE_SYM(__USER_LABEL_PREFIX__, lzma_crc32_table)
 
 /*
@@ -82,6 +82,9 @@ init_table(void)
 
 	.text
 	.globl	LZMA_CRC32
+#ifdef __ELF__
+	.hidden	LZMA_CRC32
+#endif
 
 #if !defined(__APPLE__) && !defined(_WIN32) && !defined(__CYGWIN__) \
 		&& !defined(__MSDOS__)
@@ -290,14 +293,7 @@ LZMA_CRC32:
 	.indirect_symbol LZMA_CRC32_TABLE
 	.long 0
 
-#elif defined(_WIN32) || defined(__CYGWIN__)
-#	ifdef DLL_EXPORT
-	/* This is equivalent of __declspec(dllexport). */
-	.section .drectve
-	.ascii " -export:lzma_crc32"
-#	endif
-
-#elif !defined(__MSDOS__)
+#elif !defined(_WIN32) && !defined(__CYGWIN__) && !defined(__MSDOS__)
 	/* ELF */
 	.size	LZMA_CRC32, .-LZMA_CRC32
 #endif
diff --git a/src/liblzma/check/crc64_fast.c b/src/liblzma/check/crc64_fast.c
index 82389aa8..8a6770a4 100644
--- a/src/liblzma/check/crc64_fast.c
+++ b/src/liblzma/check/crc64_fast.c
@@ -25,6 +25,18 @@
 // Generic slice-by-four CRC64 //
 /////////////////////////////////
 
+#if defined(WORDS_BIGENDIAN)
+#	include "crc64_table_be.h"
+#else
+#	include "crc64_table_le.h"
+#endif
+
+
+#ifdef HAVE_CRC_X86_ASM
+extern uint64_t lzma_crc64_generic(
+		const uint8_t *buf, size_t size, uint64_t crc);
+#else
+
 #ifdef WORDS_BIGENDIAN
 #	define A1(x) ((x) >> 56)
 #else
@@ -78,7 +90,8 @@ lzma_crc64_generic(const uint8_t *buf, size_t size, uint64_t crc)
 
 	return ~crc;
 }
-#endif
+#endif // HAVE_CRC_X86_ASM
+#endif // CRC64_GENERIC
 
 
 #if defined(CRC64_GENERIC) && defined(CRC64_ARCH_OPTIMIZED)
@@ -148,9 +161,6 @@ lzma_crc64(const uint8_t *buf, size_t size, uint64_t crc)
 	// If arch-optimized version is used unconditionally without runtime
 	// CPU detection then omitting the generic version and its 8 KiB
 	// lookup table makes the library smaller.
-	//
-	// FIXME: Lookup table isn't currently omitted on 32-bit x86,
-	// see crc64_table.c.
 	return crc64_arch_optimized(buf, size, crc);
 
 #else
diff --git a/src/liblzma/check/crc64_table.c b/src/liblzma/check/crc64_table.c
deleted file mode 100644
index 78e42759..00000000
--- a/src/liblzma/check/crc64_table.c
+++ /dev/null
@@ -1,37 +0,0 @@
-// SPDX-License-Identifier: 0BSD
-
-///////////////////////////////////////////////////////////////////////////////
-//
-/// \file       crc64_table.c
-/// \brief      Precalculated CRC64 table with correct endianness
-//
-//  Author:     Lasse Collin
-//
-///////////////////////////////////////////////////////////////////////////////
-
-#include "common.h"
-
-
-// FIXME: Compared to crc_common.h this has to check for __x86_64__ too
-// so that in 32-bit builds crc64_x86.S won't break due to a missing table.
-#if defined(HAVE_USABLE_CLMUL) && ((defined(__x86_64__) && defined(__SSSE3__) \
-			&& defined(__SSE4_1__) && defined(__PCLMUL__)) \
-		|| (defined(__e2k__) && __iset__ >= 6))
-#	define NO_CRC64_TABLE
-#endif
-
-
-#ifdef NO_CRC64_TABLE
-// No table needed. Use a typedef to avoid an empty translation unit.
-typedef void lzma_crc64_dummy;
-
-#else
-// Having the declaration here silences clang -Wmissing-variable-declarations.
-extern const uint64_t lzma_crc64_table[4][256];
-
-#	if defined(WORDS_BIGENDIAN)
-#		include "crc64_table_be.h"
-#	else
-#		include "crc64_table_le.h"
-#	endif
-#endif
diff --git a/src/liblzma/check/crc64_x86.S b/src/liblzma/check/crc64_x86.S
index 47f60818..df500186 100644
--- a/src/liblzma/check/crc64_x86.S
+++ b/src/liblzma/check/crc64_x86.S
@@ -57,7 +57,7 @@ init_table(void)
 #endif
 #define MAKE_SYM_CAT(prefix, sym) prefix ## sym
 #define MAKE_SYM(prefix, sym) MAKE_SYM_CAT(prefix, sym)
-#define LZMA_CRC64 MAKE_SYM(__USER_LABEL_PREFIX__, lzma_crc64)
+#define LZMA_CRC64 MAKE_SYM(__USER_LABEL_PREFIX__, lzma_crc64_generic)
 #define LZMA_CRC64_TABLE MAKE_SYM(__USER_LABEL_PREFIX__, lzma_crc64_table)
 
 /*
@@ -72,6 +72,9 @@ init_table(void)
 
 	.text
 	.globl	LZMA_CRC64
+#ifdef __ELF__
+	.hidden	LZMA_CRC64
+#endif
 
 #if !defined(__APPLE__) && !defined(_WIN32) && !defined(__CYGWIN__) \
 		&& !defined(__MSDOS__)
@@ -273,14 +276,7 @@ LZMA_CRC64:
 	.indirect_symbol LZMA_CRC64_TABLE
 	.long 0
 
-#elif defined(_WIN32) || defined(__CYGWIN__)
-#	ifdef DLL_EXPORT
-	/* This is equivalent of __declspec(dllexport). */
-	.section .drectve
-	.ascii " -export:lzma_crc64"
-#	endif
-
-#elif !defined(__MSDOS__)
+#elif !defined(_WIN32) && !defined(__CYGWIN__) && !defined(__MSDOS__)
 	/* ELF */
 	.size	LZMA_CRC64, .-LZMA_CRC64
 #endif
diff --git a/src/liblzma/check/crc_common.h b/src/liblzma/check/crc_common.h
index 7106646f..6a4a8d16 100644
--- a/src/liblzma/check/crc_common.h
+++ b/src/liblzma/check/crc_common.h
@@ -62,9 +62,6 @@
 // ARM64 CRC32 instruction is only useful for CRC32. Currently, only
 // little endian is supported since we were unable to test on a big
 // endian machine.
-//
-// NOTE: Keep this and the next check in sync with the macro
-//       NO_CRC32_TABLE in crc32_table.c
 #if defined(HAVE_ARM64_CRC32) && !defined(WORDS_BIGENDIAN)
 	// Allow ARM64 CRC32 instruction without a runtime check if
 	// __ARM_FEATURE_CRC32 is defined. GCC and Clang only define
@@ -81,12 +78,17 @@
 
 #if defined(HAVE_USABLE_CLMUL)
 // If CLMUL is allowed unconditionally in the compiler options then the
-// generic version can be omitted. Note that this doesn't work with MSVC
-// as I don't know how to detect the features here.
+// generic version and the tables can be omitted. Exceptions:
 //
-// NOTE: Keep this in sync with the NO_CRC32_TABLE macro in crc32_table.c
-// and NO_CRC64_TABLE in crc64_table.c.
-#	if (defined(__SSSE3__) && defined(__SSE4_1__) && defined(__PCLMUL__)) \
+//   - If 32-bit x86 assembly files are enabled then those are always
+//     built and runtime detection is used even if compiler flags
+//     were set to allow CLMUL unconditionally.
+//
+//   - This doesn't work with MSVC as I don't know how to detect
+//     the features here.
+//
+#	if (defined(__SSSE3__) && defined(__SSE4_1__) && defined(__PCLMUL__) \
+			&& !defined(HAVE_CRC_X86_ASM)) \
 		|| (defined(__e2k__) && __iset__ >= 6)
 #		define CRC32_ARCH_OPTIMIZED 1
 #		define CRC64_ARCH_OPTIMIZED 1
diff --git a/src/liblzma/check/crc_x86_clmul.h b/src/liblzma/check/crc_x86_clmul.h
index 92647654..b302d6cf 100644
--- a/src/liblzma/check/crc_x86_clmul.h
+++ b/src/liblzma/check/crc_x86_clmul.h
@@ -18,11 +18,6 @@
 /// can be built at a time. The version to build is selected by defining
 /// BUILDING_CRC_CLMUL to 32 or 64 before including this file.
 ///
-/// FIXME: Builds for 32-bit x86 use the assembly .S files by default
-/// unless configured with --disable-assembler. Even then the lookup table
-/// isn't omitted in crc64_table.c since it doesn't know that assembly
-/// code has been disabled.
-///
 /// NOTE: The x86 CLMUL CRC implementation was rewritten for XZ Utils 5.8.0.
 //
 //  Authors:    Lasse Collin
diff --git a/src/liblzma/lz/lz_encoder.c b/src/liblzma/lz/lz_encoder.c
index 4af23e14..e5c4057d 100644
--- a/src/liblzma/lz/lz_encoder.c
+++ b/src/liblzma/lz/lz_encoder.c
@@ -15,7 +15,7 @@
 
 // See lz_encoder_hash.h. This is a bit hackish but avoids making
 // endianness a conditional in makefiles.
-#if defined(WORDS_BIGENDIAN) && !defined(HAVE_SMALL)
+#ifdef LZMA_LZ_HASH_TABLE_IS_NEEDED
 #	include "lz_encoder_hash_table.h"
 #endif
 
diff --git a/src/liblzma/lz/lz_encoder_hash.h b/src/liblzma/lz/lz_encoder_hash.h
index 8ace82b0..6020b183 100644
--- a/src/liblzma/lz/lz_encoder_hash.h
+++ b/src/liblzma/lz/lz_encoder_hash.h
@@ -5,23 +5,37 @@
 /// \file       lz_encoder_hash.h
 /// \brief      Hash macros for match finders
 //
-//  Author:     Igor Pavlov
+//  Authors:    Igor Pavlov
+//              Lasse Collin
 //
 ///////////////////////////////////////////////////////////////////////////////
 
 #ifndef LZMA_LZ_ENCODER_HASH_H
 #define LZMA_LZ_ENCODER_HASH_H
 
-#if defined(WORDS_BIGENDIAN) && !defined(HAVE_SMALL)
-	// This is to make liblzma produce the same output on big endian
-	// systems that it does on little endian systems. lz_encoder.c
-	// takes care of including the actual table.
+// We need to know if CRC32_GENERIC is defined.
+#include "crc_common.h"
+
+// If HAVE_SMALL is defined, then lzma_crc32_table[][] exists and
+// it's little endian even on big endian systems.
+//
+// If HAVE_SMALL isn't defined, lzma_crc32_table[][] is in native endian
+// but we want a little endian one so that the compressed output won't
+// depend on the processor endianness. Big endian systems are less common
+// so those get the burden of an extra 1 KiB table.
+//
+// If HAVE_SMALL isn't defined and CRC32_GENERIC isn't defined either,
+// then lzma_crc32_table[][] doesn't exist.
+#if defined(HAVE_SMALL) \
+		|| (defined(CRC32_GENERIC) && !defined(WORDS_BIGENDIAN))
+#	include "check.h"
+#	define hash_table lzma_crc32_table[0]
+#else
+	// lz_encoder.c takes care of including the actual table.
 	lzma_attr_visibility_hidden
 	extern const uint32_t lzma_lz_hash_table[256];
 #	define hash_table lzma_lz_hash_table
-#else
-#	include "check.h"
-#	define hash_table lzma_crc32_table[0]
+#	define LZMA_LZ_HASH_TABLE_IS_NEEDED 1
 #endif
 
 #define HASH_2_SIZE (UINT32_C(1) << 10)