diff --git a/src/liblzma/common/file_info.c b/src/liblzma/common/file_info.c
index c14a2819..57d720d3 100644
--- a/src/liblzma/common/file_info.c
+++ b/src/liblzma/common/file_info.c
@@ -438,7 +438,8 @@ file_info_decode(void *coder_ptr, const lzma_allocator *allocator,
 		return_if_error(lzma_index_decoder_init(
 				&coder->index_decoder, allocator,
 				&coder->this_index,
-				coder->memlimit - memused));
+				coder->memlimit - memused,
+				coder->footer_flags.backward_size));
 
 		coder->index_remaining = coder->footer_flags.backward_size;
 		coder->sequence = SEQ_INDEX_DECODE;
@@ -719,8 +720,8 @@ file_info_decoder_memconfig(void *coder_ptr, uint64_t *memusage,
 
 	// combined_index_memusage + this_index_memusage shouldn't overflow
 	// because combined_index_memusage is limited by how much can be
-	// successfully allocated, and this_index_memusage is limited by
-	// INDEX_RECORDS_MAX in index_decoder.c. Check for overflow anyway.
+	// successfully allocated, and this_index_memusage is limited by the
+	// input_size_max check in index_decoder.c. Check for overflow anyway.
 	if (UINT64_MAX - combined_index_memusage < this_index_memusage)
 		return LZMA_PROG_ERROR;
 
diff --git a/src/liblzma/common/index_decoder.c b/src/liblzma/common/index_decoder.c
index a279fd95..3ecb6b3e 100644
--- a/src/liblzma/common/index_decoder.c
+++ b/src/liblzma/common/index_decoder.c
@@ -39,6 +39,12 @@ typedef struct {
 	/// successful decoding.
 	lzma_index **index_ptr;
 
+	/// If Number of Records contains a value higher than this,
+	/// the Index is immediately considered to be corrupt.
+	/// This prevents us from allocating a large amount of memory
+	/// when we know that the Index isn't big.
+	lzma_vli number_of_records_max;
+
 	/// Number of Records left to decode.
 	lzma_vli count;
 
@@ -95,11 +101,8 @@ index_decode(void *coder_ptr, const lzma_allocator *allocator,
 		if (ret != LZMA_STREAM_END)
 			goto out;
 
-		// If the Number of Records field has so large value that the
-		// Index would have to be larger than LZMA_BACKWARD_SIZE_MAX,
-		// don't even try to decode the Index because clearly it's
-		// not a valid .xz file.
-		if (coder->count > INDEX_RECORDS_MAX)
+		// Reject Number of Records values that are clearly invalid.
+		if (coder->count > coder->number_of_records_max)
 			return LZMA_DATA_ERROR;
 
 		coder->pos = 0;
@@ -266,7 +269,7 @@ index_decoder_memconfig(void *coder_ptr, uint64_t *memusage,
 
 static lzma_ret
 index_decoder_reset(lzma_index_coder *coder, const lzma_allocator *allocator,
-		lzma_index **i, uint64_t memlimit)
+		lzma_index **i, uint64_t memlimit, uint64_t input_size_max)
 {
 	// Remember the pointer given by the application. We will set it
 	// to point to the decoded Index only if decoding is successful.
@@ -280,6 +283,15 @@ index_decoder_reset(lzma_index_coder *coder, const lzma_allocator *allocator,
 	if (coder->index == NULL)
 		return LZMA_MEM_ERROR;
 
+	// Approximate how many Records the Index may contain at most when
+	// we know that the Index won't be larger than input_size_max bytes.
+	// Each Record must consume at least two bytes. The CRC32 etc.
+	// consume a few bytes too, but we don't need an exact value.
+	//
+	// file_info.c knows Backward Size and passes it to us. When we have
+	// no information, input_size_max equals LZMA_BACKWARD_SIZE_MAX.
+	coder->number_of_records_max = input_size_max / 2;
+
 	// Initialize the rest.
 	coder->sequence = SEQ_INDICATOR;
 	coder->memlimit = my_max(1, memlimit);
@@ -293,7 +305,7 @@ index_decoder_reset(lzma_index_coder *coder, const lzma_allocator *allocator,
 
 extern lzma_ret
 lzma_index_decoder_init(lzma_next_coder *next, const lzma_allocator *allocator,
-		lzma_index **i, uint64_t memlimit)
+		lzma_index **i, uint64_t memlimit, uint64_t input_size_max)
 {
 	lzma_next_coder_init(&lzma_index_decoder_init, next, allocator);
 
@@ -315,7 +327,8 @@ lzma_index_decoder_init(lzma_next_coder *next, const lzma_allocator *allocator,
 		lzma_index_end(coder->index, allocator);
 	}
 
-	return index_decoder_reset(coder, allocator, i, memlimit);
+	return index_decoder_reset(
+			coder, allocator, i, memlimit, input_size_max);
 }
 
 
@@ -328,7 +341,8 @@ lzma_index_decoder(lzma_stream *strm, lzma_index **i, uint64_t memlimit)
 	if (i != NULL)
 		*i = NULL;
 
-	lzma_next_strm_init(lzma_index_decoder_init, strm, i, memlimit);
+	lzma_next_strm_init(lzma_index_decoder_init, strm, i, memlimit,
+			LZMA_BACKWARD_SIZE_MAX);
 
 	strm->internal->supported_actions[LZMA_RUN] = true;
 	strm->internal->supported_actions[LZMA_FINISH] = true;
@@ -354,7 +368,8 @@ lzma_index_buffer_decode(lzma_index **i, uint64_t *memlimit,
 
 	// Initialize the decoder.
 	lzma_index_coder coder;
-	return_if_error(index_decoder_reset(&coder, allocator, i, *memlimit));
+	return_if_error(index_decoder_reset(&coder, allocator, i, *memlimit,
+			my_min(in_size, LZMA_BACKWARD_SIZE_MAX)));
 
 	// Store the input start position so that we can restore it in case
 	// of an error.
diff --git a/src/liblzma/common/index_decoder.h b/src/liblzma/common/index_decoder.h
index 5351d2f0..fa8dc4df 100644
--- a/src/liblzma/common/index_decoder.h
+++ b/src/liblzma/common/index_decoder.h
@@ -18,7 +18,7 @@
 
 extern lzma_ret lzma_index_decoder_init(lzma_next_coder *next,
 		const lzma_allocator *allocator,
-		lzma_index **i, uint64_t memlimit);
+		lzma_index **i, uint64_t memlimit, uint64_t input_size_max);
 
 
 #endif