diff --git a/libdeflate.h b/libdeflate.h
index 1b95beb..7db75b7 100644
--- a/libdeflate.h
+++ b/libdeflate.h
@@ -44,6 +44,28 @@ deflate_compress(struct deflate_compressor *compressor,
 		 const void *in, size_t in_nbytes,
 		 void *out, size_t out_nbytes_avail);
 
+/*
+ * deflate_compress_bound() returns a worst-case upper bound on the number of
+ * bytes of compressed data that may be produced by compressing any buffer of
+ * length less than or equal to 'in_nbytes' using deflate_compress() with the
+ * specified compressor.  Mathematically, this bound will necessarily be a
+ * number greater than or equal to 'in_nbytes'.  It may be an overestimate of
+ * the true upper bound.  The return value is guaranteed to be the same for all
+ * invocations with the same compressor and same 'in_nbytes'.
+ *
+ * Note that this function is not necessary in many applications.  With
+ * block-based compression, it is usually preferable to separately store the
+ * uncompressed size of each block and to store any blocks that did not compress
+ * to less than their original size uncompressed.  In that scenario, there is no
+ * need to know the worst-case compressed size, since the maximum number of
+ * bytes of compressed data that may be used would always be one less than the
+ * input length.  You can just pass a buffer of that size to deflate_compress()
+ * and store the data uncompressed if deflate_compress() returns 0, indicating
+ * that the compressed data did not fit into the provided output buffer.
+ */
+extern size_t
+deflate_compress_bound(struct deflate_compressor *compressor, size_t in_nbytes);
+
 /*
  * Like deflate_compress(), but stores the data in the zlib wrapper format.
  */
@@ -52,6 +74,13 @@ zlib_compress(struct deflate_compressor *compressor,
 	      const void *in, size_t in_nbytes,
 	      void *out, size_t out_nbytes_avail);
 
+/*
+ * Like deflate_compress_bound(), but assumes the data will be compressed with
+ * zlib_compress() rather than with deflate_compress().
+ */
+extern size_t
+zlib_compress_bound(struct deflate_compressor *compressor, size_t in_nbytes);
+
 /*
  * Like deflate_compress(), but stores the data in the gzip wrapper format.
  */
@@ -60,6 +89,13 @@ gzip_compress(struct deflate_compressor *compressor,
 	      const void *in, size_t in_nbytes,
 	      void *out, size_t out_nbytes_avail);
 
+/*
+ * Like deflate_compress_bound(), but assumes the data will be compressed with
+ * gzip_compress() rather than with deflate_compress().
+ */
+extern size_t
+gzip_compress_bound(struct deflate_compressor *compressor, size_t in_nbytes);
+
 /*
  * deflate_free_compressor() frees a DEFLATE compressor that was allocated with
  * deflate_alloc_compressor().  If a NULL pointer is passed in, no action is
diff --git a/src/deflate_compress.c b/src/deflate_compress.c
index 57a3613..0fdcb9b 100644
--- a/src/deflate_compress.c
+++ b/src/deflate_compress.c
@@ -2512,8 +2512,17 @@ deflate_compress(struct deflate_compressor *c,
 		 const void *in, size_t in_nbytes,
 		 void *out, size_t out_nbytes_avail)
 {
-	if (in_nbytes < 16 || out_nbytes_avail < MIN_OUTPUT_SIZE)
+	if (unlikely(out_nbytes_avail < MIN_OUTPUT_SIZE))
 		return 0;
+	if (unlikely(in_nbytes == 0)) {
+		/* Empty input; output a single empty block.  */
+		struct deflate_output_bitstream os;
+		deflate_init_output(&os, out, out_nbytes_avail);
+		deflate_reset_symbol_frequencies(c);
+		deflate_finish_sequence(c->sequences, 0);
+		deflate_write_block(c, &os, in, 0, true);
+		return deflate_flush_output(&os);
+	}
 	return (*c->impl)(c, in, in_nbytes, out, out_nbytes_avail);
 }
 
@@ -2528,3 +2537,16 @@ deflate_get_compression_level(struct deflate_compressor *c)
 {
 	return c->compression_level;
 }
+
+/* Return an upper bound on the compressed size for compressing @in_nbytes bytes
+ * of data.  This function needs some work to be more accurate.  */
+LIBEXPORT size_t
+deflate_compress_bound(struct deflate_compressor *c, size_t in_nbytes)
+{
+	size_t max_num_blocks =
+		(in_nbytes + MAX_ITEMS_PER_BLOCK - 1) / MAX_ITEMS_PER_BLOCK;
+	if (max_num_blocks == 0)
+		max_num_blocks++;
+	return MIN_OUTPUT_SIZE + (in_nbytes * 9 + 7) / 8 +
+		max_num_blocks * 200;
+}
diff --git a/src/gzip_compress.c b/src/gzip_compress.c
index 8129718..cb60448 100644
--- a/src/gzip_compress.c
+++ b/src/gzip_compress.c
@@ -66,3 +66,9 @@ gzip_compress(struct deflate_compressor *c, const void *in, size_t in_size,
 
 	return out_next - (u8 *)out;
 }
+
+LIBEXPORT size_t
+gzip_compress_bound(struct deflate_compressor *c, size_t in_nbytes)
+{
+	return GZIP_MIN_OVERHEAD + deflate_compress_bound(c, in_nbytes);
+}
diff --git a/src/zlib_compress.c b/src/zlib_compress.c
index 1a3f039..79765cf 100644
--- a/src/zlib_compress.c
+++ b/src/zlib_compress.c
@@ -58,3 +58,9 @@ zlib_compress(struct deflate_compressor *c, const void *in, size_t in_size,
 
 	return out_next - (u8 *)out;
 }
+
+LIBEXPORT size_t
+zlib_compress_bound(struct deflate_compressor *c, size_t in_nbytes)
+{
+	return ZLIB_MIN_OVERHEAD + deflate_compress_bound(c, in_nbytes);
+}