diff --git a/tests/rest.rs b/tests/rest.rs
index 96d6b67f..ce49feb7 100644
--- a/tests/rest.rs
+++ b/tests/rest.rs
@@ -313,22 +313,35 @@ fn test_rest() -> Result<()> {
 
         // Test GET /block/:hash
         {
-            let bestblockhash = get_plain("/blocks/tip/hash")?;
-            let block = get_json(&format!("/block/{}", bestblockhash))?;
+            let block1_hash = get_plain("/block-height/1")?;
+            let block1 = get_json(&format!("/block/{}", block1_hash))?;
 
             // No PoW-related stuff
-            assert!(block["bits"].is_null());
-            assert!(block["nonce"].is_null());
-            assert!(block["difficulty"].is_null());
+            assert!(block1["bits"].is_null());
+            assert!(block1["nonce"].is_null());
+            assert!(block1["difficulty"].is_null());
 
             // Dynamic Federations (dynafed) fields
-            assert!(block["ext"]["current"]["signblockscript"].is_string());
-            assert!(block["ext"]["current"]["fedpegscript"].is_string());
-            assert!(block["ext"]["current"]["fedpeg_program"].is_string());
-            assert!(block["ext"]["current"]["signblock_witness_limit"].is_u64());
-            assert!(block["ext"]["current"]["extension_space"].is_array());
-            assert!(block["ext"]["proposed"].is_object());
-            assert!(block["ext"]["signblock_witness"].is_array());
+            // Block #1 should have the Full dynafed params
+            // See https://docs.rs/elements/latest/elements/dynafed/enum.Params.html
+            assert!(block1["ext"]["current"]["signblockscript"].is_string());
+            assert!(block1["ext"]["current"]["fedpegscript"].is_string());
+            assert!(block1["ext"]["current"]["fedpeg_program"].is_string());
+            assert!(block1["ext"]["current"]["signblock_witness_limit"].is_u64());
+            assert!(block1["ext"]["current"]["extension_space"].is_array());
+            assert!(block1["ext"]["proposed"].is_object());
+            assert!(block1["ext"]["signblock_witness"].is_array());
+
+            // Block #2 should have the Compact params
+            let block2_hash = get_plain("/block-height/2")?;
+            let block2 = get_json(&format!("/block/{}", block2_hash))?;
+            assert!(block2["ext"]["current"]["signblockscript"].is_string());
+            assert!(block2["ext"]["current"]["signblock_witness_limit"].is_u64());
+            // With the `elided_root` in place of `fedpegscript`/`fedpeg_program`/`extension_space``
+            assert!(block2["ext"]["current"]["elided_root"].is_string());
+            assert!(block2["ext"]["current"]["fedpegscript"].is_null());
+            assert!(block2["ext"]["current"]["fedpeg_program"].is_null());
+            assert!(block2["ext"]["current"]["extension_space"].is_null());
         }
     }