diff --git a/README.md b/README.md
index 0cfcea5ce..f8142e6ca 100644
--- a/README.md
+++ b/README.md
@@ -23,30 +23,38 @@ is a TL;DR:
 
 ```
 $ sudo apt-get install libsecp256k1-dev
-$ python3 -m pip install --user ".[gui,crypto]"
+$ ELECTRUM_ECC_DONT_COMPILE=1 python3 -m pip install --user ".[gui,crypto]"
 ```
 
 ### Not pure-python dependencies
 
+#### Qt GUI
+
 If you want to use the Qt interface, install the Qt dependencies:
 ```
 $ sudo apt-get install python3-pyqt6
 ```
 
+#### libsecp256k1
+
 For elliptic curve operations,
 [libsecp256k1](https://github.com/bitcoin-core/secp256k1)
-is a required dependency:
-```
-$ sudo apt-get install libsecp256k1-dev
-```
+is a required dependency.
 
-Alternatively, when running from a cloned repository, a script is provided to build
-libsecp256k1 yourself:
+If you "pip install" Electrum, by default libsecp will get compiled locally,
+as part of the `electrum-ecc` dependency. This can be opted-out of,
+by setting the `ELECTRUM_ECC_DONT_COMPILE=1` environment variable.
+For the compilation to work, besides a C compiler, you need at least:
 ```
 $ sudo apt-get install automake libtool
-$ ./contrib/make_libsecp256k1.sh
+```
+If you opt out of the compilation, you need to provide libsecp in another way, e.g.:
+```
+$ sudo apt-get install libsecp256k1-dev
 ```
 
+#### cryptography
+
 Due to the need for fast symmetric ciphers,
 [cryptography](https://github.com/pyca/cryptography) is required.
 Install from your package manager (or from pip):
@@ -54,6 +62,8 @@ Install from your package manager (or from pip):
 $ sudo apt-get install python3-cryptography
 ```
 
+#### hardware-wallet support
+
 If you would like hardware wallet support,
 [see this](https://github.com/spesmilo/electrum-docs/blob/master/hardware-linux.rst).
 
diff --git a/contrib/build-wine/README_windows.md b/contrib/build-wine/README_windows.md
index a34cce1f9..b6ac49ac5 100644
--- a/contrib/build-wine/README_windows.md
+++ b/contrib/build-wine/README_windows.md
@@ -21,6 +21,10 @@ Run install (this should install most dependencies):
 
 ### 2. Install `libsecp256k1`
 
+[comment]: # (technically the dll should be put into site-packages/electrum_ecc/,
+but putting it into electrum/ also works because of the `os.add_dll_directory` call in
+electrum/__init__.py)
+
 [libsecp256k1](https://github.com/bitcoin-core/secp256k1) is a required dependency.
 This is a C library, which you need to compile yourself.
 Electrum needs a dll, named `libsecp256k1-0.dll` (or newer `libsecp256k1-*.dll`),
diff --git a/contrib/osx/README_macos.md b/contrib/osx/README_macos.md
index 9549d6ed3..a56e63c8d 100644
--- a/contrib/osx/README_macos.md
+++ b/contrib/osx/README_macos.md
@@ -15,18 +15,23 @@ $ cd electrum
 $ git submodule update --init
 ```
 
-Run install (this should install most dependencies):
+### 2. Prepare for compiling libsecp256k1
+
+To be able to build the `electrum-ecc` package from source
+(which is pulled in when installing Electrum in the next step),
+you need:
 ```
-$ python3 -m pip install --user -e ".[gui,crypto]"
+$ brew install autoconf automake libtool coreutils
 ```
 
-### 2. Install libsecp256k1
+### 3. Install Electrum
+
+Run install (this should install the dependencies):
 ```
-$ brew install autoconf automake libtool coreutils
-$ contrib/make_libsecp256k1.sh
+$ python3 -m pip install --user -e ".[gui,crypto]"
 ```
 
-### 3. Run electrum:
+### 4. Run electrum:
 ```
 $ ./run_electrum
 ```