diff --git a/Cargo.toml b/Cargo.toml
index cc521ff..b0af928 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -50,7 +50,7 @@ zeroize = { version = "1.5", features = ["zeroize_derive"], optional = true }
 
 # Unexported dependnecies
 bitcoin_hashes = { version = ">=0.12, <=0.13", default-features = false }
-unicode-normalization = { version = "=0.1.22", default-features = false, optional = true }
+unicode-normalization = { version = "0.1.22", default-features = false, optional = true }
 
 [dev-dependencies]
 # Enabling the "rand" feature by default to run the benches
diff --git a/README.md b/README.md
index aecd61f..fe375ab 100644
--- a/README.md
+++ b/README.md
@@ -31,10 +31,14 @@ Use the `all-languages` feature to enable all languages.
 
 This crate supports Rust v1.41.1 and up and works with `no_std`.
 
-When using older version of Rust, you might have to pin the version of the
-`bitcoin_hashes` crate used as such:
-```
-$ cargo update --package "bitcoin_hashes" --precise "0.12.0"
+When using older version of Rust, you might have to pin the versions of several crates, for an up-to-date list refer to [`contrib/test.sh`](contrib/test.sh):
+
+```bash
+cargo update --package "bitcoin_hashes" --precise "0.12.0"
+cargo update --package "rand" --precise "0.6.0"
+cargo update --package "libc" --precise "0.2.151"
+cargo update --package "tinyvec" --precise "1.6.0"
+cargo update --package "unicode-normalization" --precise "0.1.22"
 ```
 
 If you enable the `zeroize` feature the MSRV becomes 1.51.
diff --git a/contrib/test.sh b/contrib/test.sh
index 63bf7c5..235aa0b 100755
--- a/contrib/test.sh
+++ b/contrib/test.sh
@@ -10,6 +10,10 @@ rustc --version
 # Pin dependencies as required if we are using MSRV toolchain.
 if cargo --version | grep "1\.41"; then
     cargo update --package "bitcoin_hashes" --precise "0.12.0"
+    cargo update --package "rand" --precise "0.6.0"
+    cargo update --package "libc" --precise "0.2.151"
+    cargo update --package "tinyvec" --precise "1.6.0"
+    cargo update --package "unicode-normalization" --precise "0.1.22"
 fi
 
 echo "********* Testing std *************"
@@ -37,7 +41,7 @@ then
     cargo build --verbose --no-default-features
 
     # Build std + no_std, to make sure they are not incompatible
-    cargo build --verbose 
+    cargo build --verbose
     # Test no_std
     cargo test --verbose --no-default-features