diff --git a/.travis.yml b/.travis.yml
index 0aa22be73f..210a0de329 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -116,7 +116,7 @@ jobs:
         - libbrotli-dev
         - libzstd-dev
   - env:
-    - T=debug HYPER="yes" C="--with-hyper=$HOME/hyper --with-openssl" LD_LIBRARY_PATH=$HOME/hyper/target/debug:/usr/local/lib TFLAGS="1 to 153"
+    - T=debug HYPER="yes" C="--with-hyper=$HOME/hyper --with-openssl" LD_LIBRARY_PATH=$HOME/hyper/target/debug:/usr/local/lib TFLAGS="1 to 153 220 221 222 223 224 230 232 314 315 316 396 397"
     addons:
       apt:
         <<: *common_apt
diff --git a/tests/data/test220 b/tests/data/test220
index cfc8cbda77..844bb02393 100644
--- a/tests/data/test220
+++ b/tests/data/test220
@@ -55,22 +55,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-%if hyper
-s/^Accept-Encoding: .*/Accept-Encoding: xxx
/
-%else
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
-%endif
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-%if hyper
 Accept-Encoding: xxx
-%else
-Accept-Encoding: xxx
-%endif
 
 </protocol>
 </verify>
diff --git a/tests/data/test221 b/tests/data/test221
index ce80637b10..2d769bcc76 100644
--- a/tests/data/test221
+++ b/tests/data/test221
@@ -55,14 +55,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 <errorcode>
diff --git a/tests/data/test222 b/tests/data/test222
index a06234a08b..3f6e7c97f7 100644
--- a/tests/data/test222
+++ b/tests/data/test222
@@ -186,14 +186,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 </verify>
diff --git a/tests/data/test223 b/tests/data/test223
index a37645d7d9..4d0dddc115 100644
--- a/tests/data/test223
+++ b/tests/data/test223
@@ -76,14 +76,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 <errorcode>
diff --git a/tests/data/test224 b/tests/data/test224
index f98c8eddf3..4fc84207c4 100644
--- a/tests/data/test224
+++ b/tests/data/test224
@@ -91,14 +91,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 </verify>
diff --git a/tests/data/test230 b/tests/data/test230
index ea54f9dd4b..a8c04be682 100644
--- a/tests/data/test230
+++ b/tests/data/test230
@@ -187,14 +187,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 </verify>
diff --git a/tests/data/test232 b/tests/data/test232
index a856adea21..32fdc6a350 100644
--- a/tests/data/test232
+++ b/tests/data/test232
@@ -186,14 +186,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 </verify>
diff --git a/tests/data/test314 b/tests/data/test314
index 5080ceabc0..cdc36af210 100644
--- a/tests/data/test314
+++ b/tests/data/test314
@@ -182,22 +182,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-%if hyper
-s/^Accept-Encoding: .*/Accept-Encoding: xxx
/
-%else
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
-%endif
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-%if hyper
 Accept-Encoding: xxx
-%else
-Accept-Encoding: xxx
-%endif
 
 </protocol>
 </verify>
diff --git a/tests/data/test315 b/tests/data/test315
index 62f5b29e5a..3073251e2b 100644
--- a/tests/data/test315
+++ b/tests/data/test315
@@ -72,14 +72,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 <errorcode>
diff --git a/tests/data/test316 b/tests/data/test316
index 5b26a2a9db..be7de17be3 100644
--- a/tests/data/test316
+++ b/tests/data/test316
@@ -182,14 +182,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 </verify>
diff --git a/tests/data/test396 b/tests/data/test396
index 2cd04c389b..11dd1a901e 100644
--- a/tests/data/test396
+++ b/tests/data/test396
@@ -186,14 +186,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 </verify>
diff --git a/tests/data/test397 b/tests/data/test397
index 9bc65e9941..4ad130a76b 100644
--- a/tests/data/test397
+++ b/tests/data/test397
@@ -182,14 +182,14 @@ http://%HOSTIP:%HTTPPORT/%TESTNUMBER --compressed
 # Verify data after the test has been "shot"
 <verify>
 <strippart>
-s/^Accept-Encoding: .*/Accept-Encoding: xxx/
+s/^Accept-Encoding: [a-zA-Z, ]*/Accept-Encoding: xxx/
 </strippart>
 <protocol>
 GET /%TESTNUMBER HTTP/1.1
 Host: %HOSTIP:%HTTPPORT
 User-Agent: curl/%VERSION
 Accept: */*
-Accept-Encoding: xxx
+Accept-Encoding: xxx
 
 </protocol>
 </verify>
diff --git a/tests/valgrind.supp b/tests/valgrind.supp
index 6d72a8bb40..6e570b1bf7 100644
--- a/tests/valgrind.supp
+++ b/tests/valgrind.supp
@@ -1,3 +1,12 @@
+{
+   zstd_decompression-1.3.3-on-Ubuntu-18.04_with_hyper
+   Memcheck:Cond
+   fun:ZSTD_decompressStream
+   fun:zstd_unencode_write
+   fun:Curl_unencode_write
+   fun:hyper_body_chunk
+}
+
 {
    zstd_decompression-1.3.3-on-Ubuntu-18.04
    Memcheck:Cond