diff --git a/changes/ticket40741 b/changes/ticket40741
new file mode 100644
index 0000000000..2a9f72489d
--- /dev/null
+++ b/changes/ticket40741
@@ -0,0 +1,2 @@
+  o Minor feature (lzma):
+    - Fix compiler warnings for liblzma >= 5.3.1. Closes ticket 40741.
diff --git a/src/lib/compress/compress_lzma.c b/src/lib/compress/compress_lzma.c
index 7e5c1a2883..6ae8fd8109 100644
--- a/src/lib/compress/compress_lzma.c
+++ b/src/lib/compress/compress_lzma.c
@@ -73,6 +73,23 @@ lzma_error_str(lzma_ret error)
       return "Unable to progress";
     case LZMA_PROG_ERROR:
       return "Programming error";
+#if LZMA_VERSION >= 50030010
+    case LZMA_SEEK_NEEDED:
+      // This can be returned by the .xz file_info decoder but with
+      // lzma_alone_decoder/encoder as we use, it should never be seen.
+      return "Seek needed";
+#endif
+#if LZMA_VERSION >= 50030020
+    case LZMA_RET_INTERNAL1:
+    case LZMA_RET_INTERNAL2:
+    case LZMA_RET_INTERNAL3:
+    case LZMA_RET_INTERNAL4:
+    case LZMA_RET_INTERNAL5:
+    case LZMA_RET_INTERNAL6:
+    case LZMA_RET_INTERNAL7:
+    case LZMA_RET_INTERNAL8:
+      FALLTHROUGH;
+#endif
     default:
       return "Unknown LZMA error";
   }
@@ -306,6 +323,19 @@ tor_lzma_compress_process(tor_lzma_compress_state_t *state,
     case LZMA_OPTIONS_ERROR:
     case LZMA_DATA_ERROR:
     case LZMA_PROG_ERROR:
+#if LZMA_VERSION >= 50030010
+    case LZMA_SEEK_NEEDED:
+#endif
+#if LZMA_VERSION >= 50030020
+    case LZMA_RET_INTERNAL1:
+    case LZMA_RET_INTERNAL2:
+    case LZMA_RET_INTERNAL3:
+    case LZMA_RET_INTERNAL4:
+    case LZMA_RET_INTERNAL5:
+    case LZMA_RET_INTERNAL6:
+    case LZMA_RET_INTERNAL7:
+    case LZMA_RET_INTERNAL8:
+#endif
     default:
       log_warn(LD_GENERAL, "LZMA %s didn't finish: %s.",
                state->compress ? "compression" : "decompression",